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Ignition source

2026-11-02T17:47:56Z

Peter: Improve FSE wiki article: Ignition source; source, clarity and calculation review (GPT-6)

An '''ignition source''' supplies energy capable of initiating combustion when it reaches a suitable fuel-oxidiser system. Flames, sparks, heated wires, incandescent particles and hot surfaces can act as sources. Chemical self-heating can also create an initiating condition inside a material. Effectiveness depends on the fuel, mixing, exposure and heat losses at the point of interaction.<ref name="Kanury-2-230">Kanury (2002), p. 2-230.</ref><ref name="Gray-2-211">Gray (2002), p. 2-211.</ref>

The source is only one part of [[Ignition]]. A flammable mixture and suitable thermal conditions must also be present. A source that is too small or loses energy too quickly can fail, while a modest flame or spark can initiate a much larger fire when the surrounding mixture is favourable.<ref name="Kanury-2-232">Kanury (2002), p. 2-232.</ref><ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

Ignition sources can also occur in sequence. NUREG-1805 describes a burning wastebasket becoming a source for a chair, after which the chair can ignite other fuel. The initial device and subsequent burning objects therefore play different roles in the developing fire. Every later burning object must be assessed both as a target and as a potential new source.<ref name="NUREG-1805-F37">Iqbal and Salley (2004), p. F-37.</ref>
[[File:fse-ignition-source-v2.svg|thumb|upright=1.5|alt=Wastebasket ignites a chair and the chair becomes a source for another object.|Burning objects can become later ignition sources. Based on Iqbal and Salley (2004), p. F-37.]]

== Flames, sparks and hot surfaces ==

A small pilot flame initiates a reaction in an already suitable fuel-air mixture. Its role is not necessarily to heat the whole fuel body or generate all the pyrolysis gases. Once the reaction begins, it can propagate away from the pilot through the connected mixture.<ref name="Kanury-2-230" />

Sparks and heated filaments can perform a similar pilot function. Their effect depends on energy, size, exposure time and the thermal and chemical properties of the mixture. Heat loss to surrounding gas and surfaces can quench the initial reaction before propagation develops.<ref name="Kanury-2-232" />

Hot surfaces create a different exposure because they can heat a fuel continuously. Surface temperature alone does not determine ignition: contact area, airflow, fuel thickness and exposure duration affect the energy balance. A small hot object can therefore produce a different outcome from a large surface at the same nominal temperature.<ref name="Kanury-2-231">Kanury (2002), pp. 2-231–2-232.</ref>

Open flames introduce both a pilot and a heat source for further fuel production. They can ignite a gas mixture rapidly or heat liquids and solids until vapour and pyrolysis products become involved. These distinct roles should be identified when reconstructing a fire scenario.<ref name="Kanury-2-230" /><ref name="VR-4.1">Van Rossum (2027), §4.1.</ref>

Electrical faults can produce local overheating or arcing. In one NUREG-1805 case, improperly grounded equipment caused fault current to overheat conductors and ignite material in two locations. This nuclear-plant incident illustrates a specific electrical sequence, not a universal frequency for cable ignition.<ref name="NUREG-1805-H24">Iqbal and Salley (2004), pp. H-24–H-25.</ref>

[[Hot work]] includes activities using heat, sparks or open flame, such as cutting, welding and grinding. These activities can introduce an ignition source into areas where it is not normally present. Fuel arrangement and work procedures therefore form part of the source assessment.<ref name="NUREG-1805-F37" /><ref name="NUREG-6850-6-21">EPRI and NRC (2005), p. 6-21.</ref>

Oxygen-acetylene torches provide a particularly intense source. NUREG-1805 gives a hottest-flame value of approximately 3,500 °C for the torch conditions described. That value concerns the flame itself and does not equal the temperature reached by every target or the energy required for ignition.<ref name="NUREG-1805-3-9">Iqbal and Salley (2004), p. 3-9.</ref>

The Electric Power Research Institute (EPRI) and U.S. Nuclear Regulatory Commission (NRC) address welding and cutting in their 2005 nuclear fire-analysis methodology. They link frequency with maintenance activity, hot-work procedures and housekeeping. It treats these as plant-specific influences rather than fixed properties of a compartment. Similar reasoning applies to temporary work in other settings, although the numerical bins are specific to the nuclear method.<ref name="NUREG-6850-6-21" />

A continuous fire watch can shorten detection time when hot work ignites fuel. The same guidance states that such fires are likely to be detected quickly when a watch has been posted. This is a response measure, not proof that ignition has been prevented.<ref name="NUREG-6850-11-28">EPRI and NRC (2005), p. 11-28.</ref>

== Ignition energy and flammable atmospheres ==

[[Minimum ignition energy]] is the lowest energy associated with ignition of a specified fuel-oxidiser mixture under stated conditions. It is relevant when a spark or other short-duration source contacts a flammable atmosphere. Mixture composition, temperature and the nature of the discharge affect the requirement.<ref name="Kanury-2-232" /><ref name="Zalosh-3-405">Zalosh (2002), p. 3-405.</ref>

The 2005 International Fire Engineering Guidelines note that fuel-air mixtures within the flammable region can often be ignited by sources of only millijoules. The actual value depends on the mixture and test method. A small electrical or static source can therefore be significant even without a large hot surface.<ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref>

Flammability limits remain essential when interpreting this energy. Outside the propagating range, a source can create local combustion without a flame travelling through the wider mixture. Beyler distinguishes this local effect from sustained flame propagation within the limits.<ref name="Beyler-2-172">Beyler (2002), pp. 2-172–2-173.</ref>

Prevention commonly keeps gas or vapour concentrations well below the lower flammable limit. The guidelines caution against relying on a mixture above the upper limit because subsequent dilution can return it to the flammable region. Ignition-source control works together with concentration control rather than replacing it.<ref name="IFEG-3.3-2" />

== Self-heating as an internal source ==

[[Self-heating]] occurs when chemical reactions inside a material generate energy faster than it can be lost. The material then supplies part of the initiating heat itself. Poor thermal conductivity and insulating containers can help retain this energy.<ref name="Gray-2-211" />

The critical condition depends on material chemistry, ambient temperature, size and shape. Larger bodies can favour runaway because heat is retained more effectively, while higher ambient temperature reduces the relative thermal driving force for cooling. No single external ignition device is required in these cases.<ref name="Gray-2-211" /><ref name="Gray-2-212">Gray (2002), p. 2-212.</ref>
[[File:fse-ignition-source-v3.svg|thumb|upright=1.5|alt=Heat generated inside a body exceeds losses and produces internal runaway.|Self-heating can create an internal ignition source. Based on Gray (2002), pp. 2-211–2-212.]]

Preheated products add another variable. Hot laundry, recently manufactured chipboard and hot porous food products require attention to the material's own stacking temperature as well as ambient conditions. Gray explains that time to ignition can be much shorter for preheated bodies than for material stacked at ambient temperature.<ref name="Gray-2-211" /><ref name="Gray-2-213">Gray (2002), p. 2-213.</ref>

Spontaneous runaway often begins at the centre of a low-conductivity body. Charring or ash can therefore be found inside while the exterior appears less affected. This evidence can inform investigation, but it must be assessed alongside other possible ignition sources and preheating.<ref name="Gray-2-212" />

== Source and target interaction ==

The target is the fuel exposed to the source. Its physical and chemical properties determine how it responds, including conductivity, heat capacity, decomposition behaviour and geometry. A source-target description should retain these properties rather than treating ignition as a property of the source alone.<ref name="Kanury-2-229">Kanury (2002), p. 2-229.</ref>
[[File:fse-ignition-source-v1.svg|thumb|upright=1.5|alt=Source heating a target while vapour, oxygen and heat losses shape ignition.|Ignition depends on source-target interaction and heat loss. Based on Kanury (2002), pp. 2-230–2-232.]]

For a solid, incoming energy is partitioned into internal conduction, reradiation and convection to adjacent gas. Moisture evaporation and pyrolysis then modify the response. The source can be steady in the model while the net heating of the target changes substantially over time.<ref name="Kanury-2-232" />

Mixing has a dual effect. It is necessary to bring fuel vapour and oxygen together, but it can also cool and dilute the mixture. Spontaneous ignition needs both suitable composition and sufficient thermal condition at the same location. More airflow is therefore not always more favourable.<ref name="Kanury-2-232" />

For piloted ignition, the pilot can be small relative to the target because it only initiates the reaction. It still cannot be infinitely small: reaction can be quenched if the source region does not exceed the mixture's critical dimensions and energy requirements. The relevant threshold belongs to the whole mixture-source arrangement.<ref name="Kanury-2-232" />

Source position can also change the fire that follows ignition. NUREG-1805 contrasts a pilot at the bottom of a curtain with the same pilot at the top. The first arrangement favours rapid upward flame spread, while the second produces slower downward spread. Source identification therefore includes its location relative to the fuel, as well as the device or energy type.<ref name="NUREG-1805-6-3">Iqbal and Salley (2004), p. 6-3.</ref>

== Fire statistics and frequency analysis ==

[[Fire statistics]] can show which sources and first-ignited materials occur in reported incidents. Such evidence helps prioritise prevention and estimate ignition frequencies. It does not by itself establish the cause of an individual fire or the probability of ignition during one particular exposure.<ref name="IFEG-2.4-4" /><ref name="NUREG-6850-6-21" />

Nuclear fire probabilistic risk analysis uses detailed ignition-source counts and weighting factors. The method considers equipment, maintenance, occupancy and storage when assigning compartment-specific influences. These categories belong to US nuclear power plant analysis and should not be presented as universal building values.<ref name="NUREG-6850-6-21" />

The 2005 guidance recommends work-order counts and staff information to assess maintenance-related transient fires. It separately addresses welding and cutting, including procedures that prohibit these activities during power operation. This demonstrates how administrative controls can alter the frequency assigned to a source scenario.<ref name="NUREG-6850-6-22">EPRI and NRC (2005), p. 6-22.</ref>

Data quality remains important. The 2005 guidelines note that ignition statistics can support quantitative frequency studies and qualitative comparisons, but general prediction of ignition potential remained uncertain. Source identification and statistical frequency answer different questions.<ref name="IFEG-2.4-4" />

== Hazardous areas and prevention ==

For [[Hazardous area classification]], the source inventory has to be related to the potential presence of a flammable atmosphere. The IFEG gas and vapour discussion identifies mixture concentration as a separate part of ignition prevention. Removing one possible source does not establish that the atmosphere is outside its flammable range.<ref name="IFEG-3.3-2" />

Prevention can address an activity, the flammable atmosphere or the separation of fuel from energy. Detection and response act on a fire after ignition. The suitable combination depends on whether the source is permanent equipment, a temporary task or an internal reaction. One generic prohibition cannot cover all these mechanisms.<ref name="IFEG-2.4-4" /><ref name="NUREG-6850-6-21" />

Hot-work procedures provide a temporary-source example. Housekeeping addresses available fuel, work controls address source generation and a posted fire watch can shorten detection time. Evaluating only the torch or spark would miss the wider scenario that determines whether a small ignition becomes a damaging fire.<ref name="NUREG-6850-6-21" /><ref name="NUREG-6850-11-28" />

For self-heating storage, source prevention can involve size, stacking temperature and heat dissipation rather than electrical exclusion. The source is distributed within the fuel body, so separating it from the fuel is not a meaningful description. Geometry and storage conditions become the principal controls.<ref name="Gray-2-211" />

== Fire investigation ==

[[Fire investigation]] seeks to establish the sequence and conditions of ignition from evidence. Potential sources are evaluated together with target materials, heat transfer and subsequent fire development. Finding a device capable of ignition is not alone proof that it initiated the event.<ref name="Kanury-2-229" /><ref name="Gray-2-212" />

Electrical evidence can include fault paths and conductor damage. The Palo Verde incident in NUREG-1805 linked simultaneous fires to a common overheated conductor caused by grounding faults. The value of that example lies in tracing the complete sequence rather than assigning every cable fire to an electrical fault without evidence.<ref name="NUREG-1805-H24" />

Self-heating evidence can include deep central charring and a comparatively intact exterior. Gray nevertheless stresses the need to consider solar exposure, recent processing and other preheating. Unknown cause can also be more common in large destructive fires because evidence is lost.<ref name="Gray-2-211" /><ref name="Gray-2-212" />

A reliable investigation distinguishes initial ignition from later sources. A burning object found at one location may have started the fire there or may itself have been ignited by an earlier object. Reconstructing this order prevents the first discovered burning item from being misidentified as the original igniter.<ref name="NUREG-1805-F37" />

== Calculating electrical source energy ==

A theoretical energy calculation is useful when the source is a simple electrical discharge. It describes the energy associated with the circuit, which can be compared with ignition-test evidence for a specified mixture. The discharge type must match the test. Zalosh distinguishes capacitive electrostatic discharges from inductive sparks because their duration and ignition effectiveness differ.<ref name="Zalosh-3-405" />

For a purely capacitive discharge, energy depends on capacitance and the square of the voltage before discharge. Capacitance describes how much electrical charge a body stores for a given voltage. The equation is an idealised electrical relation, rather than a complete calculation of heat deposited in a particular fuel mixture.<ref name="Zalosh-3-405" />

<math display="block">E=\frac{1}{2}CV^2</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>E</math> || Theoretical energy of the capacitive discharge || J
|-
| <math>C</math> || Electrical capacitance || F
|-
| <math>V</math> || Voltage before discharge || V
|}

Zalosh's worked example considers an elevated powder silo with a capacitance of 500 pF. The example powder has an ignition energy of 10 mJ for inductive sparks and 50 mJ for capacitive sparks. The capacitive comparison therefore uses 50 mJ. These are the supplied example's values, not general properties of pharmaceutical powders or storage silos.<ref name="Zalosh-3-405" />

Rearranging the energy equation gives the voltage associated with that capacitive ignition energy. Converting picofarads to farads and millijoules to joules gives approximately 14 kV. The calculation retains the unrounded value until the final result. Its meaning is a threshold comparison for the idealised source and specified powder in the example.<ref name="Zalosh-3-405" />

<math display="block">V=\sqrt{\frac{2E}{C}}=\sqrt{\frac{2(50\times10^{-3})}{500\times10^{-12}}}=14142\ldots\;\mathrm{V}\approx14\;\mathrm{kV}</math>

Using the inductive value in this capacitive calculation would compare unlike discharge conditions. Zalosh explains that longer-duration sparks can ignite a dust cloud at lower energy than a short capacitive discharge. Dust concentration and mixture temperature also influence the measured threshold. The numerical energy alone therefore does not fully characterise the source's ignition capability.<ref name="Zalosh-3-405" />

The same equation does not quantify ignition by frictional sparks, glowing particles or hot surfaces. Their heating histories and contact mechanisms differ from a purely capacitive discharge. Zalosh notes that evaluating mechanical friction and impact sparks is more difficult. Kanury's source-target description likewise requires the thermal and chemical conditions at the actual interaction.<ref name="Zalosh-3-405" /><ref name="Kanury-2-232" />

== See also ==

* [[Fire triangle]]
* [[Photovoltaic system fire]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L. (2002). Flammability limits of premixed and diffusion flames. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-172–2-187). National Fire Protection Association.
* Electric Power Research Institute, & U.S. Nuclear Regulatory Commission. (2005). ''EPRI/NRC-RES fire PRA methodology for nuclear power facilities: Volume 2: Detailed methodology'' (EPRI 1011989; NUREG/CR-6850).
* Gray, B. (2002). Spontaneous combustion and self-heating. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-211–2-228). National Fire Protection Association.
* Iqbal, N., & Salley, M. H. (2004). ''Fire dynamics tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission fire protection inspection program'' (NUREG-1805). U.S. Nuclear Regulatory Commission.
* Kanury, A. M. (2002). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-229–2-245). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.
* Zalosh, R. (2002). Explosion protection. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-402–3-421). National Fire Protection Association.

[[Category:Ignition & Flame Spread]]

Ignition

2026-11-02T17:44:05Z

Peter: Improve FSE wiki article: Ignition; source, clarity and calculation review (GPT-6)

'''Ignition''' is the initiation of combustion in a fuel-oxidiser system. It can produce a flame, glowing combustion or smouldering, depending on the fuel and exposure. Initial combustion may be brief or may persist after external heating is removed. Its onset depends on fuel production, mixing with oxygen, temperature, reaction rate and heat loss.<ref name="Kanury-2-188">Kanury (2002b), p. 2-188.</ref><ref name="Kanury-2-230">Kanury (2002a), p. 2-230.</ref>

An ignition source and an ignitable material are therefore not sufficient as separate labels. Their interaction must produce suitable conditions in the same place and at the same time. A spark can fail near a poorly mixed vapour cloud, while a weaker source can succeed within a suitable mixture.<ref name="Kanury-2-230" /><ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

Ignition is also a stage within fire development rather than a complete description of the later fire. The initial reaction does not determine subsequent flame spread or the involvement of an entire enclosure. Persistent flaming requires continuing fuel and heat feedback, while transient ignition can produce a flame that disappears when external heating is removed. Prevention, detection and suppression depend on which of these conditions has been reached.<ref name="Kanury-2-230" />

== Piloted, non-piloted and self-induced ignition ==

Piloted ignition uses a local hot object or energy source such as a flame or spark to initiate combustion in a prepared fuel-air mixture. The pilot is not necessarily responsible for heating the entire solid or producing all its fuel gases. Its principal role is to start a reaction that can then propagate.<ref name="IFEG-2.4-4" /><ref name="Kanury-2-230" />
[[File:fse-ignition-v1.svg|thumb|upright=1.5|alt=Three routes: pilot, hot mixture without pilot and internal self-heating.|Three ignition modes with different initiating conditions. Based on Australian Building Codes Board et al. (2005), p. 2.4-4.]]

Non-piloted ignition occurs when the fuel-vapour and oxygen mixture reaches a condition in which it ignites without that local pilot. Temperature and composition remain essential, and heat losses must not prevent the reaction from accelerating. The absence of a visible flame before ignition does not mean that no energy was supplied.<ref name="IFEG-2.4-4" /><ref name="Kanury-2-232">Kanury (2002a), p. 2-232.</ref>

Self-induced ignition begins with oxidation inside a solid material. These reactions release energy, increasing decomposition and temperature until the critical condition is crossed. The process is often associated with heat being retained by poor conduction through the material or its container.<ref name="IFEG-2.4-4" /><ref name="Gray-2-211">Gray (2002), p. 2-211.</ref>

[[Self-heating]] describes this internal rise caused by chemical heat generation exceeding heat loss. Larger bodies and higher ambient temperatures can favour criticality by reducing relative heat loss. The result depends on material chemistry, size, shape and initial temperature rather than on one universal ambient threshold.<ref name="Gray-2-211" /><ref name="Gray-2-212">Gray (2002), p. 2-212.</ref>

== Fuel gases, liquids and solids ==

For gaseous fuels, composition and mixing are immediate concerns. Fuel and oxidiser must occur within a flammable range, and the ignition source must exceed the mixture's requirements. The flame can then propagate through the connected mixture rather than remaining only at the source.<ref name="Beyler-2-172">Beyler (2002), pp. 2-172–2-173.</ref><ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref>

Liquids usually have to evaporate before flaming combustion. The vapour above the surface mixes with air and can flash when piloted. Sustained burning requires enough heat feedback to maintain evaporation after the initial flash. Liquid bulk temperature, volatility, ventilation and container geometry all affect this sequence.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref><ref name="Kanury-2-190">Kanury (2002b), p. 2-190.</ref>

Many solids require [[Pyrolysis]] before they can support a gas-phase flame. Heating decomposes the material and releases volatile products, often leaving char. These volatiles mix with oxygen in the boundary layer and ignite when their composition and thermal condition are suitable.<ref name="VR-3.1">Van Rossum (2027), §3.1.</ref><ref name="Kanury-2-232" />

The solid's thermal response therefore forms only one part of ignition. Kanury groups the problem into production of combustible gases, their mixing with oxidant and induction of a sufficiently rapid, self-supporting reaction. Material properties, geometry and gas flow influence all three stages.<ref name="Kanury-2-230" />

Smouldering and glowing are different combustion modes. Smouldering involves subsurface or surface oxidation in a porous fuel, while flaming occurs in the gas phase. A fire scenario should not assume that every ignition immediately produces a visible flame.<ref name="Kanury-2-230" /><ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

== Heat exposure and ignition time ==

[[Critical heat flux for ignition]] can be estimated by extrapolating ignition-test data towards an indefinitely long ignition time. It is a parameter of the fitted model, distinct from an experimentally determined minimum flux. A surface can absorb energy while simultaneously losing heat through conduction, convection and radiation.<ref name="NUREG-1805-6-5">Iqbal and Salley (2004), p. 6-5.</ref><ref name="Kanury-2-231">Kanury (2002a), pp. 2-231–2-232.</ref>

At the start of radiant heating, energy arriving at a solid is divided between conduction into the interior, reradiation and convective heating of nearby gas. Moisture evaporation and later pyrolysis change this partition. The surface and interior consequently follow different temperature histories.<ref name="Kanury-2-232" />
[[File:fse-ignition-v2.svg|thumb|upright=1.5|alt=Radiant heat dividing into solid conduction, reradiation and convection before pyrolysis.|Energy partition during heating and ignition. Based on Kanury (2002a), p. 2-232.]]

[[Time to ignition]] is the exposure duration needed to cross the ignition condition. It depends on heating intensity, material response, thickness, initial temperature and whether transient or persistent ignition is sought. Longer exposure at lower intensity cannot always be traded directly against shorter exposure at higher intensity.<ref name="Kanury-2-230" /><ref name="Kanury-2-231" />

Kanury's discussion of Martin's map distinguishes nonignition, glowing ignition, transient ignition and persistent ignition regions for the tested cellulosic arrangements. Thin specimens can ignite quickly without producing persistent flaming, while thick specimens can lose energy into their interior. At very high exposure, surface ablation can occur without ignition in the mapped conditions.<ref name="Kanury-2-231" />

The 2005 International Fire Engineering Guidelines note that direct flame contact with a second item is sometimes treated conservatively as immediate ignition. This simplification ignores the time actually required for pyrolysis and heating of decomposition products. It is a modelling choice for that context, not a universal physical observation.<ref name="IFEG-2.4-4" />

== Autoignition and critical conditions ==

[[Autoignition temperature]] is associated with ignition of a gas or vapour mixture without a pilot under specified test conditions. It differs from the temperature of a hot surface or from the bulk temperature of every reacting solid. Test geometry, pressure and exposure can affect the measured result.<ref name="Kanury-2-189">Kanury (2002b), pp. 2-189–2-190.</ref>

Self-heating bodies have a critical condition representing a watershed between stable subcritical behaviour and thermal runaway. Chemical reaction rates can rise steeply with temperature, while heat loss changes more gradually. Once generation exceeds loss sufficiently, internal temperature can accelerate upwards.<ref name="Gray-2-211" /><ref name="Gray-2-212" />

Critical ambient temperature is used when body size is fixed, while critical size or diameter is relevant when ambient temperature is fixed. Preheated materials introduce a further stacking-temperature consideration. These variables show why one material cannot be assigned a universal spontaneous-ignition temperature in every storage arrangement.<ref name="Gray-2-211" />

The location of runaway is often internal. Gray describes charring or ash at the centre while the exterior remains comparatively intact in some spontaneously ignited bodies. Such deep-seated combustion can be difficult to extinguish and can reignite after apparent suppression.<ref name="Gray-2-212" />

[[Flash point]] describes a liquid temperature at which the vapour-air mixture just above the surface supports a momentary flash under a specified piloted test. The flame can sweep through the mixture and then go out. It does not yet demonstrate persistent combustion of the liquid.<ref name="Kanury-2-190" />

Fire point instead requires self-sustained burning. This distinction mirrors Kanury's broader separation of transient and persistent ignition. An engineering assessment should therefore state whether it concerns the first observable reaction, a propagating flame or a fire that continues after the source is removed.<ref name="Kanury-2-190" /><ref name="Kanury-2-230" />

Smouldering can also precede later flaming. Transition requires a flammable pyrolysis-gas mixture and sufficient heat to ignite it at the same location and time. Enhanced oxygen supply, reduced heat loss and local geometry can promote this change, but it is not an automatic stage of every smouldering fire.<ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

== Ignition sources and the fire triangle ==

An [[Ignition source]] supplies the local energy or reactive condition needed to initiate combustion. Examples include a small flame, heated wire, electric spark or incandescent particle. The source's effectiveness depends on the mixture it contacts and on heat lost to the surroundings.<ref name="Kanury-2-230" /><ref name="Kanury-2-232" />

The [[Fire triangle]] places ignition source within the wider combination of fuel, oxygen and heat. Most building environments already contain fuel and oxygen, so qualitative prevention often focuses on separating them from open flames, sparks and sufficiently hot surfaces. The model remains a checklist rather than an ignition-time calculation.<ref name="IFEG-2.4-4" />

For gases and vapours, avoiding flammable concentrations is a principal strategy. The 2005 guidelines recommend keeping concentrations well below the lower flammable limit rather than relying on a rich mixture remaining above the upper limit. Dilution can move a rich mixture back into the ignitable range.<ref name="IFEG-3.3-2" />

Ignition can also pass from one object to another. NUREG-1805 uses the example of a burning wastebasket igniting a chair, which can then ignite further fuel. The initial igniter and subsequent burning objects become sources in a sequence, so the fire history is not limited to the first device.<ref name="NUREG-1805-F37">Iqbal and Salley (2004), p. F-37.</ref>

== Measurements and material data ==

Ignition tests impose controlled radiant or convective exposure and observe the response. The measured temperature, heat flux and time depend on apparatus, specimen thickness, backing and pilot arrangement. Results should retain these conditions instead of being reduced to an unqualified material label.<ref name="Kanury-2-229">Kanury (2002a), p. 2-229.</ref><ref name="Kanury-2-231" />

The 2005 guidelines list grouped ignition-temperature ranges for several solid categories. Wood, paper and cotton are listed at 250 to 365 °C for piloted ignition and 250 to 400 °C for autoignition. These older grouped values illustrate variability and should not be used as universal thresholds for every product and exposure.<ref name="IFEG-3.3-4">Australian Building Codes Board et al. (2005), p. 3.3-4.</ref>
[[File:fse-ignition-v3.svg|thumb|upright=1.5|alt=Wood, paper and cotton group: piloted 250 to 365 °C and autoignition 250 to 400 °C.|Grouped ignition-temperature ranges in the 2005 IFEG. Based on Australian Building Codes Board et al. (2005), p. 3.3-4.]]

Exposure duration changes the appropriate data. The guidelines note that many wood studies used exposures of 20 minutes or less and provide a lower heat-flux result from a day-long exposure. Long-term self-heating requires a different treatment again, including the size of the stored aggregation.<ref name="IFEG-3.3-4-5">Australian Building Codes Board et al. (2005), pp. 3.3-4–3.3-5.</ref>

Material properties also change during heating. Moisture leaves, char forms and some polymers melt before decomposition. These changes affect heat transport and volatile release, so an ignition model based on unchanged properties can apply only within its stated assumptions.<ref name="Kanury-2-232" /><ref name="Beyler-Hirschler-1-112">Beyler and Hirschler (2002), pp. 1-112–1-113.</ref>

== Prevention and engineering assessment ==

Prevention can address fuel condition, oxidiser concentration, ignition energy and heat retention. Keeping work areas free of unnecessary combustibles, controlling flammable atmospheres and separating hot surfaces from fuel each acts on a different part of the ignition problem. Their suitability depends on the scenario.<ref name="IFEG-2.4-4" /><ref name="IFEG-3.3-2" />

For subsequent items, radiant exposure depends on the burning item and separation distance. The 2005 guidelines describe a simplified pre-flashover method in which radiation from the upper layer and room surfaces is neglected and only flame radiation from the first item is included. That assumption must not be transferred to a developed compartment fire.<ref name="IFEG-2.4-4" />

Probabilistic studies can use fire statistics for ignition frequency by building class and ignited material. The 2005 guidelines state that general quantitative methods for predicting ignition potential were not available in that document. Statistical frequencies support analysis but do not replace scenario-specific assessment of sources and fuels.<ref name="IFEG-2.4-4" />

Self-heating requires particular caution in extrapolation. Gray warns that time to ignition is highly sensitive to material, size, initial temperature and distance from the critical condition. Hot stacked material can ignite much sooner than a simple ambient-temperature model predicts.<ref name="Gray-2-212" /><ref name="Gray-2-213">Gray (2002), p. 2-213.</ref>

== Calculating ignition under radiant heating ==

For a thermally thick solid under constant radiant exposure, a simplified correlation estimates the time needed for piloted ignition. Thermally thick means that the interior remains appreciably cooler during the relevant heating period. The model combines the external heat flux with two properties fitted from ignition tests. Both properties must belong to the same material and correlation.<ref name="NUREG-1805-6-5" /><ref name="NUREG-1805-6-7">Iqbal and Salley (2004), p. 6-7.</ref>

The thermal response parameter represents resistance to surface heating. Subtracting the fitted critical heat flux from the external exposure represents the margin of heating above that model's threshold. In the Tewarson method reproduced in NUREG-1805, ignition time depends on the square of their ratio. The equation applies during transient heating before steady conditions develop.<ref name="Tewarson-as-cited">Tewarson (1995), as cited in Iqbal and Salley (2004), pp. 6-4–6-6.</ref>

<math display="block">t_{ig}=\frac{\pi}{4}\left(\frac{\mathrm{TRP}}{\dot q''_e-\mathrm{CHF}}\right)^2</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>t_{ig}</math> || Calculated time to piloted ignition || s
|-
| <math>\mathrm{TRP}</math> || Thermal response parameter from the specified correlation || kW·s<sup>1/2</sup>/m²
|-
| <math>\dot q''_e</math> || Constant external radiant heat flux || kW/m²
|-
| <math>\mathrm{CHF}</math> || Critical heat flux estimated from that correlation || kW/m²
|}

For red oak, the report lists a critical heat flux of 10 kW/m² and a thermal response parameter of 134 kW·s<sup>1/2</sup>/m². Choose a constant external exposure of 30 kW/m² for this illustrative calculation. Substituting the tabulated material values gives about 35 s to ignition. The result represents the stated model and exposure, rather than a measured ignition time for every oak product.<ref name="Tewarson-as-cited" />

<math display="block">t_{ig}=\frac{\pi}{4}\left(\frac{134}{30-10}\right)^2=35.256\ldots\;\mathrm{s}\approx35\;\mathrm{s}</math>

At a chosen exposure of 20 kW/m², the same calculation gives approximately 140 s. Halving the margin above the critical heat flux multiplies the predicted ignition time by four. This illustrates why a heat-flux value needs an exposure duration when assessing ignition. The unrounded calculation is retained until the final reported time.<ref name="Tewarson-as-cited" />

The equation is used only above the fitted critical flux. At or below that value, substituting numbers does not yield a valid ignition-time prediction. Near the threshold, the estimate becomes highly sensitive to the flux and fitted properties. A positive result produced by squaring a negative denominator would have no physical meaning in this model.<ref name="NUREG-1805-6-5" />

The report explicitly distinguishes the extrapolated critical flux from the minimum flux observed under practical conditions. Other correlations fit the data differently and produce different effective properties. Substituting a thermal response parameter from one method into another can therefore destroy the connection with the tests. Variable heating, thin specimens and long-duration self-heating also require separate treatment.<ref name="NUREG-1805-6-5" /><ref name="NUREG-1805-6-7" /><ref name="IFEG-3.3-4-5" />

An ignition calculation predicts a specified observation, such as the appearance of piloted flaming. It does not establish that the fire will persist after the source is removed or spread to another item. Forced pyrolysis may produce smoke before combustion, while smouldering can begin without a visible flame. Those different outcomes need their own observation criteria.<ref name="Kanury-2-230" /><ref name="Ohlemiller-2-200" />

== See also ==

* [[Firebrands]]
* [[Flame spread]]
* [[Smouldering-to-flaming transition]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L. (2002). Flammability limits of premixed and diffusion flames. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-172–2-187). National Fire Protection Association.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Gray, B. (2002). Spontaneous combustion and self-heating. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-211–2-228). National Fire Protection Association.
* Iqbal, N., & Salley, M. H. (2004). ''Fire dynamics tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission fire protection inspection program'' (NUREG-1805). U.S. Nuclear Regulatory Commission.
* Kanury, A. M. (2002a). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-229–2-245). National Fire Protection Association.
* Kanury, A. M. (2002b). Ignition of liquid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-188–2-199). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Ignition & Flame Spread]]

Thermal radiation

2026-11-02T17:43:57Z

Peter: Improve FSE wiki article: Thermal radiation; source, clarity and calculation review (GPT-6)

'''Thermal radiation''' is heat transfer by electromagnetic waves emitted because of the temperature of matter. It can occur through a vacuum and does not require a transporting medium between source and receiver. In fires, radiation comes from flames, hot soot, combustion gases and heated solid or liquid surfaces.<ref name="VR-5.4">Van Rossum (2027), §5.4.</ref><ref name="Tien-1-73">Tien, Lee, and Stretton (2002), p. 1-73.</ref>

This mechanism can heat objects at a distance, support ignition and contribute to fire spread within and between enclosures. Its importance increases strongly with temperature and can also change with fire scale. Radiation therefore forms a distinct part of [[Heat transfer]], alongside conduction and convection.<ref name="VR-5.4" /><ref name="Tien-1-73" />

The heat flux received by an object is not determined by source temperature alone. Emission, absorption, reflection, geometry, orientation and the medium between the surfaces can all influence the result. A useful assessment identifies both the radiant source and the receiving surface.<ref name="Tien-1-75">Tien, Lee, and Stretton (2002), p. 1-75.</ref>

== Electromagnetic energy and temperature ==

Every material above absolute zero emits radiation. The relevant energy can be described using electromagnetic waves or photons, and its distribution varies with wavelength. At temperatures relevant to buildings and fires, the dominant thermal-radiation range lies mainly in infrared, with some visible contribution at higher temperatures.<ref name="VR-5.4" />

Tien and colleagues identify a major thermal-radiation spectrum of 1 to 100 micrometres for the fire applications discussed. Water vapour and carbon dioxide can absorb and emit strongly in parts of this range. Hydrocarbon gases and soot also participate, with soot often contributing more than gases in the situations described.<ref name="Tien-1-73" />
[[File:fse-thermal-radiation-v1.svg|thumb|upright=1.5|alt=Hot source emitting infrared through gas to a receiver with absorption and reradiation.|Thermal radiation involves source, medium and receiver. Based on Van Rossum (2027), §5.4 and Tien, Lee, and Stretton (2002), p. 1-73.]]

Visible glow is only one part of radiant emission. Van Rossum notes that a surface at approximately 550 °C can emit enough visible radiation to appear red-hot, with colour changing as temperature rises further. Infrared energy can nevertheless be transferred without a surface appearing luminous to human vision.<ref name="VR-5.4" />

The wavelength of maximum blackbody emission shifts towards shorter wavelengths as temperature increases. This relationship, known as Wien's displacement law, shows why the spectral distribution changes with temperature. It does not mean that all energy moves to the visible range at fire temperatures.<ref name="Tien-1-74">Tien, Lee, and Stretton (2002), p. 1-74.</ref>

Radiation can be absorbed or emitted by gases between surfaces. Van Rossum notes that these gases can warm and reradiate, or absorb part of the energy passing through them. A clear line of sight therefore does not guarantee that the intervening medium has no effect.<ref name="VR-5.4" />

== Emission, absorption and reflection ==

[[Emissivity]] describes how strongly a real surface emits compared with an ideal blackbody under corresponding conditions. A blackbody is an idealised perfect absorber and emitter. Real materials have emissivities that can depend on wavelength, surface condition and temperature.<ref name="VR-5.4" /><ref name="Tien-1-74" />

Engineering calculations often use one emissivity value rather than a full wavelength-dependent description. Van Rossum explains that this grey-surface simplification avoids integrating detailed properties across the spectrum, which are difficult to determine. The simplification is practical but remains an approximation.<ref name="VR-5.4" />
[[File:fse-thermal-radiation-v3.svg|thumb|upright=1.5|alt=Emissivity values: polished aluminium 0.04, anodised aluminium 0.9 and rough concrete 0.91.|Emissivity varies with material and surface finish. Based on Van Rossum (2027), §5.4.]]

Surface finish can make a substantial difference. The example table in Van Rossum lists polished aluminium at 0.04 and anodised aluminium at 0.9, while rough concrete is listed at 0.91 and human skin at 0.97 to 0.999. These values demonstrate why identical substrate names or colours do not establish radiant behaviour.<ref name="VR-5.4" />

Kirchhoff's law connects absorptivity and emissivity under specified equilibrium and spectral conditions. It supports the intuitive relationship that good absorbers can also be good emitters. Applying total rather than spectral properties requires additional assumptions about the incident radiation and surface behaviour.<ref name="Tien-1-75" />

Incoming radiation can be absorbed, reflected or transmitted. Solids and liquids commonly absorb within a very small surface depth, while porous insulation can also transfer energy internally through radiation. Van Rossum notes that this contribution is commonly included in an effective conductivity rather than calculated separately.<ref name="VR-5.4" />

== Temperature and emitted power ==

The [[Stefan-Boltzmann law]] relates ideal blackbody emission per unit area to the fourth power of absolute temperature. Real-surface calculations include emissivity, and net exchange also accounts for radiation received from the surroundings. Kelvin, not degrees Celsius, must be used for the absolute-temperature relationship.<ref name="VR-5.4" /><ref name="Tien-1-74" />

For a source represented by a single temperature and emissivity, emitted power per unit area is calculated from the following expression. Setting emissivity to one gives the blackbody limit. The source's emissivity scales that maximum emission. This is an emission calculation, before the distance and orientation of a receiver are considered.<ref name="VR-5.4" />

<math display="block">E_s=\varepsilon_s\sigma T_s^4</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>E_s</math> || Source radiant emission per unit area || W/m²
|-
| <math>\varepsilon_s</math> || Effective source emissivity || Dimensionless
|-
| <math>\sigma</math> || Stefan–Boltzmann constant, <math>5.67\times10^{-8}</math> || W/(m²·K⁴)
|-
| <math>T_s</math> || Absolute source temperature || K
|}

This fourth-power dependence explains why radiation becomes increasingly important at high temperature. Van Rossum gives a broad transition in which convection tends to dominate at lower temperatures and radiation becomes particularly important from around 400 °C. This is guidance rather than a sharp universal boundary.<ref name="VR-5.4" />

Net exchange differs from gross emission. A hot surface emits towards a cooler one, but the cooler surface also emits back. When the receiver temperature is not negligible relative to the source, considering both temperatures gives a more appropriate description of net transfer.<ref name="VR-5.4" />

The same principle applies to hot smoke layers and flames. Their emission depends on temperature and radiative properties, while receiving objects have their own temperature and properties. A calculation based only on flame temperature cannot describe the entire exchange.<ref name="Tien-1-73" /><ref name="VR-5.4" />

Temperature distribution within a flame is not uniform. Different regions and soot concentrations can produce different emission, and small flames may lose a larger proportion through convection. Radiative source models therefore simplify a spatially varying physical system.<ref name="Simmons-1-145">Simmons (2002), p. 1-145.</ref><ref name="Tien-1-73" />

== Geometry and view between surfaces ==

[[View factor]] is a geometric fraction describing the radiation leaving one surface that is intercepted by another. It depends on size, separation and orientation. It does not include emissivity, temperature or absorption by an intervening gas, which must be treated separately.<ref name="Tien-1-75" />

Two surfaces facing each other directly have a different radiant relationship from surfaces at an angle or partly screened by obstacles. Moving a receiver can consequently change heat flux even when the source remains unchanged. The physical arrangement belongs in the radiation model.<ref name="Tien-1-75" />
[[File:fse-thermal-radiation-v2.svg|thumb|upright=1.5|alt=Three receivers with different distance, angle and shielding from one source.|View factor depends on geometry, not source temperature. Based on Tien, Lee, and Stretton (2002), p. 1-75.]]

A diffuse source emits with equal intensity per apparent surface area in each outward direction. For a uniform diffuse source, its direct contribution to receiver irradiation follows from a view factor. This assumes the gap neither absorbs, emits nor scatters radiation. The factor is defined from the receiver towards the source, describing the source's share of the receiver's radiative view. Reflections and other emitting surfaces are excluded from this direct contribution.<ref name="Tien-1-75" /><ref name="Tien-1-76">Tien, Lee, and Stretton (2002), p. 1-76.</ref>

<math display="block">G_{\mathrm{direct}}=F_{r\rightarrow s}E_s</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>G_{\mathrm{direct}}</math> || Direct source radiation incident on the receiver || W/m²
|-
| <math>F_{r\rightarrow s}</math> || View factor from receiver to source || Dimensionless
|}

The direction of the view factor matters. The fraction of a large source's radiation reaching a small target is generally different from the target's view of that source. The two factors are related through the areas of the surfaces. Using the wrong direction can therefore give the wrong flux per unit receiver area.<ref name="Tien-1-76" />

=== Emitted and received radiation in a source example ===

Van Rossum considers a square smoke layer measuring 49 m by 49 m in a 16 m high space. The layer is 2 m deep, at 400 °C, with an assumed emissivity of 0.9. A small upward-facing target is located centrally at a height of 1.75 m. These conditions provide a worked illustration of emission and geometric interception.<ref name="VR-5.4" />

The separation between the target and the layer underside is 12.25 m. Dividing the layer into four equal rectangles gives the source's tabulated view factor of 0.208 per rectangle, totalling 0.832. The source temperature is 673.15 K. Using those inputs gives the following emitted and direct incident fluxes, calculated without intermediate rounding.<ref name="VR-5.4" />

<math display="block">E_s=0.9\times5.67\times10^{-8}\times673.15^4\approx10.5\ \mathrm{kW/m^2}</math>

<math display="block">G_{\mathrm{direct}}=0.832E_s\approx8.72\ \mathrm{kW/m^2}</math>

The second result is radiation arriving from the layer, before accounting for receiver absorption and emission. It is not the net heat gained by the target. Van Rossum's separate net-exchange calculation also includes a receiver temperature and therefore gives a different quantity. Other emitting surfaces, reflections or absorption in the intervening gas would require additional terms.<ref name="VR-5.4" /><ref name="Tien-1-76" />

For an opaque receiver, net radiative heating is absorbed irradiation minus the receiver's own emission. The total incident irradiation includes every relevant source and reflection. Absorptivity describes the fraction absorbed from that incident radiation, while emissivity describes emission at the receiver temperature. They are not interchangeable without the appropriate spectral assumptions.<ref name="Tien-1-75" /><ref name="Tien-1-76" />

<math display="block">\dot q''_{\mathrm{rad,net}}=\alpha_rG_{\mathrm{total}}-\varepsilon_r\sigma T_r^4</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot q''_{\mathrm{rad,net}}</math> || Net radiative heat flux into the receiver || W/m²
|-
| <math>\alpha_r</math> || Effective receiver absorptivity for the incident radiation || Dimensionless
|-
| <math>G_{\mathrm{total}}</math> || Total radiation incident on the receiver || W/m²
|-
| <math>\varepsilon_r</math> || Receiver emissivity || Dimensionless
|-
| <math>T_r</math> || Absolute receiver temperature || K
|}

Geometry also affects how radiation contributes to compartment feedback. Hot upper gases and heated boundaries can expose many lower surfaces simultaneously. An object need not be above the flame or in the convective plume to receive this energy.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Tien-1-75" />

== Flame radiation and fire spread ==

[[Flame radiation]] arises from luminous gases, soot and the hot reaction region. Hot soot particles are responsible for much of the yellow or orange light in many diffusion flames, but low luminosity does not imply negligible thermal radiation. Source temperature, soot and gas properties all contribute.<ref name="VR-4.3" /><ref name="Tien-1-73" />

Radiative feedback supports evaporation and pyrolysis, allowing flames to sustain or extend fuel production. Along a vertical surface, heating above the burning region can accelerate upward spread. Radiation is therefore part of the coupling between the flame and its fuel.<ref name="VR-4.3" /><ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

[[Fire spread between buildings]] can occur when radiant energy from one fire heats combustible material across a separation. The receiving exposure depends on source size and properties, distance, orientation and screening. A gap alone does not quantify safety, and radiation need not require smoke or flames to cross it.<ref name="Tien-1-75" /><ref name="IFEG-2.6">Australian Building Codes Board et al. (2005), pp. 2.6-11–2.6-12.</ref>

Scale changes the radiative share. Tien and colleagues state that radiation is dominant in flames with characteristic lengths exceeding 0.2 m in their discussed context, while convection is more significant below that scale. Reduced-scale tests can therefore underrepresent full-scale radiant exposure if this difference is ignored.<ref name="Tien-1-73" />

Radiation can also expose people and structural elements without direct flame contact. Assessment needs the receiver's response to heat flux and exposure duration, rather than an assumption that distance alone removes the hazard.<ref name="Tien-1-73" /><ref name="VR-5.1">Van Rossum (2027), §5.1.</ref>

== Compartment fires and flashover ==

In an enclosure, flames, hot gases and heated boundaries exchange radiation with contents. Heat retained by the compartment raises surface and gas temperatures, increasing the potential for further radiative heating. This feedback can involve objects well beyond the first burning item.<ref name="VR-4.3" />

[[Flashover]] is associated with the transition to widespread involvement of combustible surfaces in a compartment. Radiation from the hot upper region and boundaries is one heat-transfer mechanism that can preheat those surfaces. The transition still depends on the complete fire scenario, including fuel and ventilation.<ref name="VR-4.7">Van Rossum (2027), §4.7.</ref><ref name="VR-4.3" />

A post-flashover environment can subject structural boundaries to sustained high temperatures. Radiative exchange then acts together with convection and conduction. Considering only internal solid conduction would omit the boundary exposure driving that temperature rise.<ref name="VR-5.2">Van Rossum (2027), §5.2.</ref><ref name="Tien-1-73" />

Radiation also leaves through openings and can heat external surfaces. Fuel volatiles burning outside an enclosure can create an additional radiant source outside the original compartment. The location of heat release and exposure therefore changes with ventilation and mixing.<ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

== Measurement and engineering use ==

Radiative heat-flux measurement addresses energy arriving at a surface per unit area and time. This differs from measuring total fire heat release rate. The same fire can produce different receiver readings at different distances and orientations.<ref name="Tien-1-75" /><ref name="VR-5.4" />

A radiation calculation should state the source model, temperature, emissivity, geometry and treatment of intervening gases. Receiver temperature and properties may also be required for net exchange. Omitting these inputs makes a result difficult to reproduce or apply elsewhere.<ref name="VR-5.4" />

Material data should be checked against surface condition. Polished, oxidised, coated and rough surfaces can have very different emissivities. Values also need an appropriate spectral and temperature basis rather than selection by material name alone.<ref name="VR-5.4" /><ref name="Tien-1-75" />

The result should be combined with other heat-transfer pathways on a consistent basis. A receiver can experience radiation and convection simultaneously while conducting energy inwards. Adding these contributions requires matching area, timing and reference conditions.<ref name="VR-5.3">Van Rossum (2027), §5.3.</ref><ref name="Rockett-Milke-1-29">Rockett and Milke (2002), p. 1-29.</ref>

== Limits and common misunderstandings ==

Thermal radiation is not simply visible light. Infrared energy can dominate the transfer, and a weakly luminous flame can still present a radiant hazard. Appearance cannot substitute for temperature, property and geometry data.<ref name="VR-5.4" /><ref name="Tien-1-73" />

A blackbody is not merely a surface coloured black. It is an idealised perfect absorber and emitter used as a reference. Real surfaces with the same visible colour can have different radiative properties.<ref name="VR-5.4" /><ref name="Tien-1-74" />

View factor does not describe how hot a source is or how strongly it emits. It describes only geometric interception. Multiplying unrelated source and receiver properties without preserving that distinction can conceal incorrect assumptions.<ref name="Tien-1-75" />

Radiative losses can cool flames and hot surfaces, contributing to extinction when heat production falls below losses. The safety effect depends on the direction, receiver and timing of the exchange.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref>

Radiative properties introduce uncertainty into engineering estimates. Real surfaces can have complex directional and wavelength-dependent behaviour, while measured property data may be incomplete. Tien and colleagues describe the grey diffuse approximation as a way to manage this complexity. Its suitability still depends on the surfaces and conditions represented.<ref name="Tien-1-76" />

Spectral detail presents a related choice. A grey-surface model may be adequate for an engineering estimate, but it hides wavelength-dependent absorption and emission. Where gases or selective surfaces are important, the simplified property basis should be checked against the source conditions.<ref name="VR-5.4" /><ref name="Tien-1-75" />

Receiver response adds a separate time dependence. A surface can absorb radiation while its temperature, emissivity and conductive losses change. Repeated or prolonged exposure therefore cannot always be represented by one unchanged receiver.<ref name="Rockett-Milke-1-29" /><ref name="VR-5.4" />

== See also ==

* [[Effects of heat on people]]
* [[Fire-resistant glazing]]
* [[Flame detector]]
* [[Glass breakage in fire]]
* [[Radiative fraction]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
* Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-144–1-154). National Fire Protection Association.
* Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-73–1-89). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Physics & Heat Transfer]]

Pyrolysis

2026-11-02T17:41:08Z

Peter: Improve FSE wiki article: Pyrolysis; source, clarity and calculation review (GPT-6)

'''Pyrolysis''' is the chemical decomposition of a material caused by heating. In many organic materials, it breaks large molecules into smaller fragments. The process can produce combustible gases, liquids and a solid residue. In fire safety, pyrolysis is especially relevant because it supplies gaseous fuel for the flaming combustion of many solids, including wood and plastics.<ref name="VR-3.1">Van Rossum (2027), §3.1.</ref><ref name="Beyler-Hirschler-1-110" />

Pyrolysis is not itself combustion. It does not require oxygen, whereas combustion requires an oxidiser. The gases produced can burn immediately, burn after travelling elsewhere or remain unburnt, depending on mixing, temperature and ignition conditions. A solid can therefore emit fuel gases and smoke without yet supporting a flame.<ref name="VR-3.1" /><ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

The process links heat transfer with fire growth. External heat or flame feedback raises the material temperature, decomposition releases volatile fuel, and combustion of those volatiles can return more heat to the material. Whether this loop sustains itself depends on heat losses, material properties and oxygen availability. Fuel production, ignition and heat release therefore cannot be described by one material constant.<ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), pp. 1-110–1-111.</ref>

== Thermal decomposition and fuel production ==

Heating does not affect every material in the same way. Thermoplastics can soften and melt before substantial decomposition, while thermosetting and cellulosic materials do not pass through the same fluid state. These physical changes alter heat transport, exposed surfaces and the routes through which volatile products escape.<ref name="Beyler-Hirschler-1-112">Beyler and Hirschler (2002), p. 1-112.</ref>
[[File:fse-pyrolysis-v1.svg|thumb|upright=1.5|alt=Heated solid with char, pyrolysis region, unchanged material and escaping volatiles.|Pyrolysis produces volatiles and residue within heated material. Based on Van Rossum (2027), §3.1 and Beyler and Hirschler (2002), pp. 1-110–1-112.]]

Chemical composition also affects decomposition. Beyler and Hirschler state that its rate, mechanism and product composition depend on both the original material's chemistry and its physical properties. Natural and synthetic polymers can therefore behave differently even when they are exposed to the same nominal heating conditions.<ref name="Beyler-Hirschler-1-111">Beyler and Hirschler (2002), p. 1-111.</ref>

Breaking a polymer chain is only one possible reaction. Decomposition can remove groups attached to the chain or create new bonds between chains, a process called cross-linking. Several mechanisms may occur in the same material. Oxygen can change these reactions and their rates when it reaches the material, even though heating can also produce decomposition without oxygen.<ref name="Beyler-Hirschler-mechanisms">Beyler and Hirschler (2002), pp. 1-113–1-114.</ref>

Cellulosic materials release adsorbed water during heating before or alongside decomposition. The desorption process starts below the boiling point of water and varies with the material. This moisture movement changes the energy needed for heating and can affect the onset and rate of later decomposition.<ref name="Beyler-Hirschler-1-112" />

Some materials form carbonaceous char. Volatile gases may have to travel through this layer before reaching the surface, where hot char can cause secondary reactions. Intumescent chars can slow further thermal decomposition considerably, while other chars can continue to oxidise at higher temperatures. The residue is consequently an active part of the fire process rather than a uniform inert layer.<ref name="Beyler-Hirschler-1-110" />

Inorganic residues behave differently again. They can form glassy barriers that restrict volatile escape and protect underlying material. Where such barriers do not form, carbonaceous char can remain susceptible to surface oxidation. The type and integrity of the residue therefore influence continuing fuel production.<ref name="Beyler-Hirschler-1-110" />

== Pyrolysis and combustion ==

[[Combustion]] involves chemical reaction with an oxidiser and release of energy, while pyrolysis is decomposition caused by heating. In a typical flaming solid-fuel fire, the two occur in different regions. Pyrolysis takes place in or at the heated material, and the volatile products burn after mixing with oxygen in the gas phase.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref>

This separation explains why flaming can occur away from the original solid. Van Rossum describes oxygen-limited compartments in which pyrolysis gases burn mainly in external flames after encountering fresh air. The fuel then originates inside the compartment, but part of its combustion and heat release occurs outside.<ref name="VR-3.1" />

[[Smouldering]] must also be distinguished from pyrolysis. Ohlemiller defines smouldering as flameless combustion sustained by oxidation at the surface of a condensed-phase fuel. Forced pyrolysis caused by an external heat flux can produce gas and smoke with little or no oxidation. Smoke production alone therefore does not prove that smouldering combustion is taking place.<ref name="Ohlemiller-2-200" />

Char links the two processes. Thermal decomposition can leave a carbon-rich, porous residue that supports direct oxygen attack. Heat released by char oxidation can then sustain smouldering and drive further decomposition nearby. Pyrolysis helps create the fuel structure in which this later surface combustion occurs.<ref name="Ohlemiller-2-200" />

== Ignition and heat exposure ==

[[Ignition]] of a solid-fuel fire commonly requires pyrolysis gases to mix with air and reach ignitable conditions. Piloted ignition uses a local flame, spark or hot object. Non-piloted ignition occurs when the gas mixture is hot enough to ignite without such a pilot. Self-induced ignition starts with oxidation inside a solid that supplies energy for further heating and decomposition.<ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

[[Heat flux]] is the rate of heat transfer per unit area and is a useful way to describe exposure of a material surface. A higher imposed flux can raise temperature and accelerate decomposition, but the response also depends on heat losses and material properties. The surface temperature alone does not capture all of these processes.<ref name="Beyler-Hirschler-1-112" /><ref name="IFEG-3.3-4">Australian Building Codes Board et al. (2005), p. 3.3-4.</ref>

The 2005 International Fire Engineering Guidelines note that wood ignition is complex and not fully quantified. Their tabulated ignition temperatures for wood, paper and cotton range from 250 to 365 °C for piloted ignition and 250 to 400 °C for autoignition. These are grouped experimental values from older guidance, not universal thresholds for every product or exposure.<ref name="IFEG-3.3-4" />
[[File:fse-pyrolysis-v3.svg|thumb|upright=1.5|alt=Wood, paper and cotton group: piloted 250 to 365 °C and autoignition 250 to 400 °C.|Reported ignition-temperature ranges for wood, paper and cotton; these are not pyrolysis thresholds. Based on Australian Building Codes Board et al. (2005), p. 3.3-4.]]

Exposure duration changes the problem. The same guidelines report that many wood ignition studies used exposures of 20 minutes or less, while a day-long experiment produced a much lower heat-flux value. Prolonged heating can also involve self-heating, where material size and heat retention influence safe storage conditions. Pyrolysis must therefore be considered over the actual exposure time.<ref name="IFEG-3.3-4" />

== Burning rate and char formation ==

[[Burning rate]] describes how quickly fuel is consumed or converted during a fire. For a decomposing solid, it is connected to the rate at which heat reaches the material and volatile products are generated. Heat of combustion provides energy per unit mass, but it does not by itself determine this rate.<ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

A sustained flame supplies part of the required heat through radiation and convection. Some energy is lost to the surroundings, so fuel production continues only when feedback is sufficient. Van Rossum uses this balance to explain why materials that release substantial energy and need little energy for decomposition can burn more rapidly.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref>

A simplified steady-state heat balance relates this feedback to the mass of material converted to vapour each second. The heat of gasification is the net energy needed to convert a unit mass of material into volatiles. Dividing net heat flux by that energy gives mass loss per unit area and time. Incoming heat includes both external exposure and flame feedback, while surface reradiation reduces the net input:<ref name="Janssens-3-39">Janssens (2002), pp. 3-39–3-40.</ref><ref name="Tewarson-3-98">Tewarson (2002), p. 3-98, Equation 11.</ref>

<math display="block">\dot{m}''=\frac{\dot{q}''_{\mathrm{in}}-\dot{q}''_{\mathrm{loss}}}{L_g}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot{m}''</math> || Mass loss rate per unit exposed area || kg/(m² s)
|-
| <math>\dot{q}''_{\mathrm{in}}</math> || Combined external and flame heat flux reaching the surface || kW/m²
|-
| <math>\dot{q}''_{\mathrm{loss}}</math> || Heat flux lost by surface reradiation || kW/m²
|-
| <math>L_g</math> || Heat of gasification || kJ/kg
|}

Tewarson's worked example uses an incoming heat flux of 70 kW/m² and a surface loss of 10 kW/m². The assumed material has a heat of gasification of 1.8 kJ/g, equivalent to 1,800 kJ/kg. The calculated mass-loss flux is about 0.033 kg/(m² s):<ref name="Tewarson-example">Tewarson (2002), p. 3-101, Example 7.</ref>

<math display="block">\dot{m}''=\frac{70-10}{1{,}800}\approx0.033\ \mathrm{kg/(m^2\,s)}</math>

For the example's exposed area of 2 m², the total mass loss is about 0.067 kg/s, or 67 g/s. This result uses the unrounded mass-loss flux before multiplying by area. It estimates fuel generation under the stated heat-balance assumptions; it does not calculate ignition time or identify the chemical products.<ref name="Tewarson-example" />

The steady approximation becomes less direct when a char layer grows or exposure varies with time. Janssens notes that charring materials may take a long time to approach steady burning, or may never do so. Their effective heat of gasification and heat fluxes can change throughout the test. A single fitted average therefore needs evidence that it represents the intended material and exposure.<ref name="Janssens-3-39" />

For timber, [[Charring rate]] describes how quickly wood is converted to char. Its value depends on fire exposure, density and moisture, so it is not a universal conversion factor for gas production. The remaining char changes heat penetration and the movement of volatile products. These effects connect structural loss of uncharred wood with the continuing supply of gaseous fuel.<ref name="Kodur-Harmathy-charring">Kodur and Harmathy (2002), pp. 1-164–1-165.</ref><ref name="Beyler-Hirschler-1-110" />

Material orientation changes heat feedback. During upward flame spread on a vertical surface, heat reaches material above the burning zone and preheats it. This can accelerate decomposition and spread. A small horizontal specimen result therefore does not automatically describe a large vertical installation.<ref name="VR-4.3" />

== Plastics and other polymeric materials ==

[[Plastics in fire]] encompass thermoplastics, thermosets and elastomers with different physical and chemical responses. Thermoplastics can soften reversibly below decomposition temperature, whereas thermosets undergo irreversible changes when formed and do not melt in the same way. These distinctions affect dripping, shape retention and exposure of fresh material during heating.<ref name="Beyler-Hirschler-1-111" /><ref name="Beyler-Hirschler-1-112" />
[[File:fse-pyrolysis-v2.svg|thumb|upright=1.5|alt=Three pathways for melting, irreversible thermoset behaviour and moisture-releasing cellulosics.|Material type changes physical behaviour during thermal decomposition. Based on Beyler and Hirschler (2002), pp. 1-111–1-112.]]

Polymer composition influences both volatile products and residue. Oxygen-containing, nitrogen-containing and halogen-containing polymers have different chemical structures and decomposition pathways. The SFPE Handbook consequently treats thermal decomposition as varied and complex rather than as one universal reaction.<ref name="Beyler-Hirschler-1-111" />

Wood and paper are natural polymeric materials with substantial cellulosic content. Their thermal response includes moisture desorption, volatile production and char formation. The residual char is generally richer in carbon and has greater surface area per unit mass than the original fuel, making it susceptible to oxidation under suitable conditions.<ref name="Beyler-Hirschler-1-111" /><ref name="Ohlemiller-2-200" />

These differences prevent a single pyrolysis temperature from representing all materials. Decomposition occurs over conditions influenced by heating rate, composition and physical transformations. A material name should therefore be accompanied by the test or scenario conditions whenever its pyrolysis behaviour is used in an assessment.<ref name="Beyler-Hirschler-1-112" />

== Pyrolysis in compartment fires ==

A compartment can strengthen the feedback between decomposition and combustion. Heat retained by the enclosure warms gases and surfaces, and radiation can then reach fuel beyond the original burning item. This additional exposure can produce volatile gases from several objects at once. The fire's fuel supply therefore changes as the compartment heats.<ref name="VR-4.3" />

Multiple materials make the response more complex. Drysdale notes that fuels in a compartment can have different stoichiometric air requirements and burning rates, while radiation changes their decomposition. The total rate of heat release cannot be inferred by treating every item as an identical fuel package with one fixed response.<ref name="Drysdale-1-95" />

Ventilation influences where the products burn. Pyrolysis can continue inside fuel even when oxygen within the compartment is insufficient to oxidise all volatile gases. Some products leave through openings and burn after mixing with external air. An assessment limited to combustion inside the enclosure can then miss part of the energy released by the pyrolysed fuel.<ref name="VR-3.1" /><ref name="Drysdale-1-95" />

Schematic design fires simplify these interacting processes into selected growth, developed and decay behaviour. The 2005 guidelines describe such curves as conservative engineering representations rather than exact reproductions of natural fires. Pyrolysis data and test results provide inputs to this simplification, but do not remove the assumptions made when constructing it.<ref name="IFEG-1.2-29">Australian Building Codes Board et al. (2005), pp. 1.2-29–1.2-30.</ref>

== Engineering use and measurement ==

Thermogravimetric analysis measures how a small sample's mass changes during a defined temperature programme. The sample can be held at a selected temperature or heated at a specified rate. Differentiating the mass record gives the mass-loss rate and helps identify separate decomposition stages. The test atmosphere is also part of the result because oxygen can alter decomposition.<ref name="Beyler-Hirschler-TGA">Beyler and Hirschler (2002), pp. 1-113–1-117.</ref>

A mass-loss curve is not automatically a fire-growth curve. Its shape depends on heating rate and the decomposition that has already occurred. A small thermal-analysis specimen also lacks the changing feedback from a large flame. These limitations explain why decomposition measurements are combined with fire tests and heat-transfer information rather than used alone to predict installed-product behaviour.<ref name="Beyler-Hirschler-TGA" />

Material tests impose a defined heat flux and measure responses such as mass loss and heat release. Oxygen-consumption calorimetry estimates heat release from oxygen used, with correction associated with incomplete combustion. It measures the outcome of combustion rather than pyrolysis alone, so interpretation must separate decomposition, mixing and oxidation.<ref name="Drysdale-1-96">Drysdale (2002), pp. 1-95–1-96.</ref>

A test specimen is usually much simpler than the installed product. Thickness, joints, composite layers and orientation can alter heat penetration and volatile movement. Char formation can add further time-dependent changes. Test data consequently need to be applied to comparable configurations or supported by an appropriate model.<ref name="Beyler-Hirschler-1-110" /><ref name="Beyler-Hirschler-1-112" />

For fire-load estimates, calorific values describe potential energy in the material inventory. They do not establish how much material will decompose and burn during a given scenario. Moisture, container protection and incomplete combustion can all reduce effective energy release. Pyrolysis is one of the processes between potential inventory and observed fire severity.<ref name="IFEG-2.4-2">Australian Building Codes Board et al. (2005), pp. 2.4-2–2.4-3.</ref><ref name="VR-4.4">Van Rossum (2027), §4.4.</ref>

== Limits and common misunderstandings ==

Pyrolysis is not synonymous with melting. Melting is a physical phase change, while pyrolysis changes chemical structure and produces new substances. Some thermoplastics melt before decomposing, but other materials decompose without entering a fluid state.<ref name="Beyler-Hirschler-1-112" />

It is also not synonymous with evaporation. A liquid can vaporise without the molecular breakdown involved in pyrolysis, although both processes can supply fuel vapour to a flame. Solids that sublime or melt and evaporate require a description suited to their actual behaviour.<ref name="Kanury-2-189">Kanury (2002), p. 2-189.</ref>

The absence of oxygen does not make pyrolysis products safe. Combustible gases can travel, accumulate and ignite after finding oxygen. The location where decomposition occurs can therefore differ from the location of rapid heat release or flame.<ref name="VR-3.1" />

Charring does not necessarily mean that fuel consumption has ended. Char can protect underlying material, but it can also oxidise and sustain smouldering. Assessment needs the condition of both the residue and the remaining unburnt material.<ref name="Beyler-Hirschler-1-110" /><ref name="Ohlemiller-2-200" />

Controlled pyrolysis outside fire safety helps clarify the distinction between decomposition and burning. Charcoal production heats wood with little or no oxygen, leaving a carbon-rich porous residue after volatile products escape. The desired process is decomposition rather than immediate combustion of all released gases.<ref name="VR-3.1" />

Wood-gas production uses related decomposition and subsequent reactions to generate a combustible gas mixture. Van Rossum describes cleaning and cooling this gas before use as engine fuel. The gas is produced in one device and burned elsewhere after oxygen is supplied, illustrating the separation that can also occur between pyrolysis and flaming in a fire.<ref name="VR-3.1" />

== See also ==

* [[Timber in fire]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Janssens, M. (2002). Calorimetry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-38–3-62). National Fire Protection Association.
* Kanury, A. M. (2002). Ignition of liquid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-188–2-199). National Fire Protection Association.
* Kodur, V. K. R., & Harmathy, T. Z. (2002). Properties of building materials. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-155–1-181). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-82–3-161). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Hot work

2026-11-02T17:38:28Z

Peter: Improve FSE wiki article: Hot work; source, clarity and calculation review (GPT-6)

'''Hot work''' is activity involving heat, sparks or open flame, including cutting, welding and grinding. It introduces a temporary [[Ignition source]] into the work area and can ignite nearby or concealed combustible material. The hazard depends on the process, fuel arrangement, exposure path and the measures used to detect and control a fire.<ref name="NUREG-1805-F37">Iqbal and Salley (2004), p. F-37.</ref><ref name="Kanury-2-230">Kanury (2002), p. 2-230.</ref>

Hot-work fires are not limited to the point where the tool is used. Sparks and burning debris can reach other fuel, while hot surfaces can remain after the task. Combustible gas or vapour can also create a flammable atmosphere that requires much less ignition energy than a solid target.<ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref><ref name="Kanury-2-232">Kanury (2002), p. 2-232.</ref>

Management therefore combines fuel and atmosphere control, work procedures, detection and readiness for suppression. A fire watch can shorten response time, but it does not remove the ignition source or guarantee that ignition will be prevented.<ref name="NUREG-6850-11-28">EPRI and NRC (2005), p. 11-28.</ref>

== Heat, sparks and flames ==

Hot work can supply several kinds of ignition exposure. An open flame can act as a pilot in a flammable mixture and as a heat source for liquids and solids. Sparks and hot particles provide local energy, while heated workpieces and tools can continue transferring energy after the active task has stopped.<ref name="Kanury-2-230" /><ref name="Kanury-2-232" />
[[File:fse-hot-work-v1.svg|thumb|upright=1.5|alt=Welding and grinding sending flames, sparks and hot debris towards visible and hidden fuel.|Hot work creates several ignition pathways. Based on Iqbal and Salley (2004), p. F-37 and Kanury (2002), pp. 2-230–2-232.]]

Oxygen-acetylene torches provide a high-temperature example. NUREG-1805 gives an approximate hottest-flame temperature of 3,500 °C for the cutting and welding conditions described. This is not the temperature reached by every target, nor does it replace an assessment of heat transfer and exposure duration.<ref name="NUREG-1805-3-9">Iqbal and Salley (2004), p. 3-9.</ref>

Grinding and cutting can produce sparks without the worker intending to maintain an open flame. Their effect depends on particle condition, target material and heat loss. A small particle can ignite a suitable gas mixture but fail to ignite a thick solid that conducts heat away rapidly.<ref name="IFEG-3.3-2" /><ref name="Kanury-2-231">Kanury (2002), pp. 2-231–2-232.</ref>

The target's condition is therefore as relevant as the source. Thin materials, deposits and porous fuel beds can respond differently from bulky components. Fuel hidden behind panels or inside cavities can also change the location and timing of detection.<ref name="Kanury-2-231" /><ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

== Ignition and delayed fire development ==

A suitable fuel-air mixture can be ignited by very low energy. The 2005 International Fire Engineering Guidelines note that millijoule sources can often suffice within the flammable region. Controlling gas and vapour concentration is therefore a separate preventive task from assessing whether a solid can withstand a spark.<ref name="IFEG-3.3-2" />

For solids, heat must produce vapour or pyrolysis gases and create suitable conditions for combustion. Incoming energy is balanced against conduction, convection and radiation losses. This explains why contact time and target geometry matter alongside the visible intensity of the work.<ref name="Kanury-2-232" />

[[Smouldering]] is particularly relevant to delayed discovery. Porous and char-forming materials can support slow, flameless oxidation with limited external sign. A small initial reaction can remain within a fuel bed before conditions favour a later transition to flaming.<ref name="Ohlemiller-2-200" /><ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

A lack of immediate flame does not establish whether combustion has begun. Forced pyrolysis can produce smoke without the oxidation that sustains smouldering. Conversely, a smouldering fuel can retain enough heat to reignite when oxygen returns after temporary exclusion.<ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref><ref name="Ohlemiller-2-200" />

== Prevention and management ==

[[Fire safety management]] coordinates the temporary source with housekeeping, maintenance and emergency response. The Electric Power Research Institute (EPRI) and U.S. Nuclear Regulatory Commission (NRC) address temporary ignition sources in their 2005 nuclear fire-analysis methodology. They link transient-fire likelihood with maintenance activity, hot-work procedures and housekeeping practices. These factors vary between work areas and should be assessed for the actual task.<ref name="NUREG-6850-6-21">EPRI and NRC (2005), p. 6-21.</ref>

A [[Fire risk assessment]] connects the ignition source with the fuel it can reach and the resulting fire-development path. Concealed spaces and openings can extend that path beyond the immediate work area. The IFEG treats such spaces as part of the spread analysis when they connect with the fire enclosure.<ref name="IFEG-1.6-6">Australian Building Codes Board et al. (2005), pp. 1.6-6–1.6-7.</ref>

Fuel control can involve reducing or protecting combustible inventory and managing flammable gases and vapours. Source control can involve changing the process or where it is performed. The 2005 guidance assigns a low maintenance influence in its specialised method where welding and cutting are prohibited during power operation, illustrating the effect of preventing the temporary source from being present.<ref name="IFEG-3.3-2" /><ref name="NUREG-6850-6-22">EPRI and NRC (2005), p. 6-22.</ref>

Work-order records and staff knowledge can help establish the type and frequency of maintenance. The nuclear method uses this evidence to rank compartment-specific activity rather than assuming an identical frequency everywhere. Its numerical factors belong to US nuclear fire probabilistic risk assessment and are not universal building values.<ref name="NUREG-6850-6-21" />

Administrative control is not treated as certainty of prevention. The 2005 method notes industry evidence of failures to follow controls and therefore retains transient-fire scenarios. A low maintenance influence where welding and cutting are prohibited is different from assigning no possibility of fire. This distinction keeps the intended procedure separate from the evidence about its implementation.<ref name="NUREG-6850-6-21" /><ref name="NUREG-6850-6-22" />

The methodology also distinguishes general transient fires from those attributed specifically to welding and cutting. General transient-fire assessment uses maintenance, occupancy and storage influences. For the welding-and-cutting categories, it uses the maintenance influence alone. These are allocation rules within that US nuclear method, rather than universal weighting factors for hot work.<ref name="NUREG-6850-6-22" />

== Fire watch and suppression ==

A continuous fire watch provides human observation during the exposure period. NUREG/CR-6850 states that fires ignited during hot work are likely to be detected quickly when a watch has been posted. Early detection can reduce the time available for fire growth and for secondary combustibles to become involved.<ref name="NUREG-6850-11-28" /><ref name="NUREG-6850-S1-14-4">EPRI and NRC (2010), p. 14-4.</ref>
[[File:fse-hot-work-v2.svg|thumb|upright=1.5|alt=Timeline from hot work and ignition to watch detection and first suppression.|A fire watch can shorten detection and response after ignition. Based on EPRI and NRC (2005), p. 11-28.]]

Detection starts the response sequence, but it does not establish that suppression succeeds. The nuclear methodology assesses detection time separately from suppression timing, effectiveness and reliability. A person observing the fire may discover it quickly while still needing time to obtain access or begin applying a suppressant.<ref name="NUREG-6850-11-28" /><ref name="NUREG-6850-S1-14-4" />

A [[Fire extinguisher]] can form part of the response arrangements. The nuclear methodology records the location and characteristics of portable extinguishers alongside fixed systems and hose equipment. Later scenario-specific guidance also considers access, equipment condition and the time needed to begin suppression. Equipment presence and timely, effective use are therefore separate considerations.<ref name="NUREG-6850-11-35">EPRI and NRC (2005), p. 11-35.</ref><ref name="NUREG-6850-S1-14-4" />

Fire-watch activity should not be confused with source elimination. It addresses detection and suppression, while housekeeping and process control reduce the chance of ignition. Both parts are needed because early response can limit damage without preventing the initial fire.<ref name="NUREG-6850-11-28" /><ref name="NUREG-6850-6-21" />

== Analysis, evidence and limitations ==

Hot-work scenarios can be evaluated by tracing the complete sequence: source generation, travel to fuel, ignition, detection and suppression. Each step has conditions and possible failures. This structure helps distinguish a prevented ignition from a fire that starts but is controlled quickly.<ref name="Kanury-2-230" /><ref name="NUREG-6850-S1-14-4" />
[[File:fse-hot-work-v3.svg|thumb|upright=1.5|alt=Flowchart linking process, source travel, fuel, ignition, detection and suppression.|Hot-work assessment follows the complete event sequence. Based on Kanury (2002), p. 2-230 and EPRI and NRC (2005), pp. 6-21–6-22.]]

Fire-event data can support frequency and suppression analysis, but the scenario remains specific. NRC guidance treats maintenance activity, occupancy and storage as plant-specific influences. It also uses response exercises and scenario differences when assessing manual suppression rather than assuming one fixed response time.<ref name="NUREG-6850-6-21" /><ref name="NUREG-6850-S1-14-4" />

The cited documents address US nuclear facilities and their analytical procedures. Their hot-work examples concern maintenance-related ignition frequency and the effect of detection or suppression. These uses do not establish permit requirements or a universal post-work watch duration for ordinary buildings.<ref name="NUREG-1805-F37" /><ref name="NUREG-6850-11-28" />

Apparent extinction can leave residual heat in a smouldering fuel. Ohlemiller explains that oxygen removal alone is insufficient unless it lasts until the fuel has cooled adequately. Reintroducing oxygen before that point can permit renewed combustion. The absence of open flaming is therefore a different observation from complete cooling.<ref name="Ohlemiller-2-206" />

Documentation can preserve this sequence for review. The work location, process, nearby and concealed fuels, ventilation conditions, watch arrangements and available suppression equipment describe the scenario together. Missing any of these can make a control appear effective only because a pathway was not considered.<ref name="NUREG-6850-6-21" /><ref name="NUREG-6850-11-28" />

Changes between tasks also matter. A work area can contain different transient combustibles or ventilation conditions from its normal state, and a later task can introduce another source. Repeating an earlier assessment without checking these differences can overlook the changed exposure.<ref name="NUREG-6850-6-21" /><ref name="IFEG-3.3-2" />

The response-time evidence also depends on the scenario. The 2010 nuclear guidance compares typical and scenario-specific brigade response using factors such as location, accessibility and equipment condition. It identifies response exercises as one possible basis for those estimates. This makes a measured or justified response sequence necessary before assigning a numerical suppression benefit.<ref name="NUREG-6850-S1-14-4" />

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Electric Power Research Institute, & U.S. Nuclear Regulatory Commission. (2005). ''EPRI/NRC-RES fire PRA methodology for nuclear power facilities: Volume 2: Detailed methodology'' (EPRI 1011989; NUREG/CR-6850).
* Electric Power Research Institute, & U.S. Nuclear Regulatory Commission. (2010). ''Fire probabilistic risk assessment methods enhancements'' (EPRI 1019259; NUREG/CR-6850, Supplement 1).
* Iqbal, N., & Salley, M. H. (2004). ''Fire dynamics tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission fire protection inspection program'' (NUREG-1805). U.S. Nuclear Regulatory Commission.
* Kanury, A. M. (2002). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-229–2-245). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.

[[Category:Ignition & Flame Spread]]

Heat transfer

2026-11-02T17:36:47Z

Peter: Improve FSE wiki article: Heat transfer; source, clarity and calculation review (GPT-6)

'''Heat transfer''' is the movement of energy caused by a temperature difference. Energy passes from hotter material, gases or surfaces to cooler ones. A continuing temperature difference can maintain heat flow even when the temperatures remain steady. In fire safety, heat transfer connects combustion with heated fuel, smoke, building boundaries, structural members, people and neighbouring objects.<ref name="VR-5.1">Van Rossum (2027), §5.1.</ref>

The three mechanisms used to describe this movement are conduction, convection and thermal radiation. They can occur simultaneously and influence one another. A flame, for example, emits radiation while hot gases rise convectively and surrounding solids conduct energy away from their heated surfaces.<ref name="VR-5.1" /><ref name="Atreya-1-44">Atreya (2002), p. 1-44.</ref>

Heat transfer determines both how a fire grows and how its effects spread. Feedback heats fuel and supports further combustion, while losses cool the reaction region. The same energy can therefore be part of fire development at one location and an unwanted exposure at another.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Rockett-Milke-1-29">Rockett and Milke (2002), p. 1-29.</ref>

== The three heat-transfer mechanisms ==

[[Conduction]] transfers energy through molecular interactions within a material or between contacting materials. It allows heat to pass through a wall or structural section without bulk movement of that section. Temperature difference, material conductivity, thickness and area influence the result.<ref name="VR-5.2">Van Rossum (2027), §5.2.</ref>

[[Convection]] transports energy through the movement of gas or liquid. Hot smoke carries energy as it rises and travels, and it also exchanges heat with surfaces along its path. Natural buoyancy, wind and mechanical equipment can all contribute to the flow.<ref name="VR-5.3">Van Rossum (2027), §5.3.</ref>

[[Thermal radiation]] transfers energy by electromagnetic waves. It can cross a vacuum and does not require a transporting medium between the source and receiver. Flames, hot soot, combustion gases and heated surfaces can all participate in emission and absorption.<ref name="VR-5.4">Van Rossum (2027), §5.4.</ref><ref name="Tien-1-73">Tien, Lee, and Stretton (2002), p. 1-73.</ref>

For a uniform solid layer under steady, one-dimensional conditions, conduction follows the temperature difference between its two surfaces. Conductivity sets how readily the material transmits heat, and thickness sets the distance it must cross. The following expression gives heat flux per unit area, with positive flow from the hotter surface to the cooler surface.<ref name="VR-5.2" />

<math display="block">\dot q''_{\mathrm{cond}}=\frac{\lambda}{L}(T_{s,h}-T_{s,c})</math>

For convection, the relevant difference is between the gas and the receiving surface. The heat-transfer coefficient represents the particular flow and boundary-layer conditions. Its value can change with velocity, turbulence and fluid properties. Positive flux in the expression below means heat enters the surface.<ref name="VR-5.3" />

<math display="block">\dot q''_{\mathrm{conv}}=h_c(T_g-T_s)</math>

For radiation, a grey-source approximation uses emissivity and the fourth power of absolute temperature. This equation gives emission from the source per unit area. Geometry and the receiving surface's properties are still needed to determine what arrives and is absorbed elsewhere. Temperature must be entered in kelvin for this calculation.<ref name="VR-5.4" /><ref name="Tien-1-75">Tien, Lee, and Stretton (2002), p. 1-75.</ref>

<math display="block">E_r=\varepsilon\sigma T^4</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot q''_{\mathrm{cond}},\dot q''_{\mathrm{conv}}</math> || Conductive and convective heat flux || W/m²
|-
| <math>\lambda</math> || Material thermal conductivity || W/(m·K)
|-
| <math>L</math> || Material thickness || m
|-
| <math>T_{s,h},T_{s,c}</math> || Hot and cold solid-surface temperatures || K or °C
|-
| <math>h_c</math> || Convective heat-transfer coefficient || W/(m²·K)
|-
| <math>T_g,T_s</math> || Gas and receiving-surface temperatures || K or °C
|-
| <math>E_r</math> || Source radiant emission per unit area || W/m²
|-
| <math>\varepsilon</math> || Source emissivity || Dimensionless
|-
| <math>\sigma</math> || Stefan–Boltzmann constant, <math>5.67\times10^{-8}</math> || W/(m²·K⁴)
|-
| <math>T</math> || Absolute source temperature || K
|}

These expressions describe different parts of the heat-transfer problem. Source emission is not directly interchangeable with net radiation absorbed at a receiver. A surface balance requires the incoming radiation, absorbed fraction and outgoing radiation at that same surface. Conduction then describes energy carried into or away from the solid interior.<ref name="Tien-1-75" /><ref name="Tien-1-76">Tien, Lee, and Stretton (2002), p. 1-76.</ref><ref name="Rockett-Milke-1-29" />

Atreya notes that convection is not a fundamental molecular mode in the same sense as conduction and radiation because it combines their effects with medium motion. In practical fire analysis, however, treating all three as separate pathways helps organise the problem. Their relative importance depends on scale, temperature and geometry.<ref name="Atreya-1-44" /><ref name="Tien-1-73" />
[[File:fse-heat-transfer-v1.svg|thumb|upright=1.5|alt=Fire heating a wall by radiation, smoke by convection and the wall by conduction.|Three heat-transfer pathways in a fire. Based on Van Rossum (2027), §5.1.]]

The dominant mechanism can change during a fire. Small flames can lose a larger relative share through convection, while radiation becomes increasingly important at larger scales and higher temperatures. Van Rossum uses approximately 70% convection and 30% radiation as a rule of thumb for an open fire, while stressing that actual proportions vary.<ref name="Tien-1-73" /><ref name="VR-4.3" />
[[File:fse-heat-transfer-v3.svg|thumb|upright=1.5|alt=Rule-of-thumb bar showing about 70 percent convection and 30 percent radiation.|Approximate open-fire energy split, not a universal ratio. Based on Van Rossum (2027), §4.3.]]

== Heat flux and energy balances ==

[[Heat flux]] expresses heat transfer per unit area and time, commonly in watts per square metre. It describes the intensity of exposure at a surface rather than the total energy released by a fire. Total heat release rate, total heat flow through an object and local heat flux must be distinguished.<ref name="VR-5.2" /><ref name="VR-5.3" />

A surface energy balance accounts for energy arriving, leaving and being stored. Radiation and convection may heat the exposed side, while conduction carries energy into the solid and other losses cool it. The surface temperature changes according to the net result rather than according to one incoming term alone.<ref name="Rockett-Milke-1-29" />
[[File:fse-heat-transfer-v2.svg|thumb|upright=1.5|alt=Source, transfer paths and receiver with absorbed, stored and outgoing energy.|A receiver experiences an energy balance, not the entire fire output. Based on Rockett and Milke (2002), p. 1-29.]]

Temperature difference drives heat transfer, but equal air temperatures do not guarantee equal surface exposure. Different flow conditions alter convection, and different source geometry or surface properties alter radiation. A complete assessment therefore includes each relevant pathway.<ref name="VR-5.3" /><ref name="Tien-1-75" />

Heat loss also controls whether combustion can continue. Near a flammability limit, losses can exceed heat production and prevent a self-sustaining flame. For a solid, insufficient feedback can reduce pyrolysis and cause the fire to decline even while fuel and oxygen remain.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref><ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

== Storage and changing temperatures ==

A steady heat-transfer calculation assumes that temperatures do not change with time. Real fires are transient: heat release rate, smoke temperature and receiving-surface temperature all change. Steady calculations can estimate an order of magnitude under selected conditions, but do not reproduce the entire fire history.<ref name="VR-5.1" />

Materials store energy as their temperature rises. Density and specific heat capacity determine how much energy a given volume can store for a temperature increase. Conductivity and geometry then influence how quickly that energy moves to deeper regions.<ref name="Rockett-Milke-1-29" />

=== A worked heat-storage example ===

For approximately constant specific heat, the energy absorbed in raising a material's temperature equals its mass multiplied by specific heat and temperature rise. This relationship describes stored energy rather than the rate at which heat enters. A larger mass requires more energy for the same temperature increase. The approximation excludes additional energy needed for phase changes.<ref name="VR-3.4">Van Rossum (2027), §3.4.</ref>

<math display="block">\Delta E=m c_p\Delta T</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\Delta E</math> || Increase in stored thermal energy || J
|-
| <math>m</math> || Heated mass || kg
|-
| <math>c_p</math> || Specific heat capacity || J/(kg·K)
|-
| <math>\Delta T</math> || Temperature rise || K or °C
|}

Van Rossum uses 100 kg of steel, a specific heat of 460 J/(kg·K), and a temperature rise of 100 K. Multiplication gives an absorbed energy of 4.6 MJ. This is the amount stored under the constant-property assumption. It is not a fire heat-release rate or a prediction of the heating time.<ref name="VR-3.4" />

<math display="block">\Delta E=100\times460\times100=4.6\times10^6\ \mathrm{J}=4.6\ \mathrm{MJ}</math>

Determining the time needed requires the net heat-transfer rate over the exposure. The internal temperature distribution also matters if different parts of the steel heat at different rates. A transient conduction calculation connects the boundary exposure with those internal temperatures. The storage example alone does not establish a uniform temperature throughout an actual structural member.<ref name="Rockett-Milke-1-29" /><ref name="VR-3.4" />

[[Thermal inertia]] describes the resistance of a material's surface temperature to rapid change under heat exposure. It is associated with conductivity, density and heat capacity acting together. Materials with different thermal inertia can therefore respond differently to the same short-duration heat flux.<ref name="Rockett-Milke-1-29" /><ref name="VR-5.2" />

The initial temperature distribution matters in a transient calculation. Surface temperature or heat flux must also be specified over time, together with relevant internal changes such as moisture evaporation. These inputs make the result specific to the construction and exposure being analysed.<ref name="Rockett-Milke-1-29" />

== Heat transfer in fire development ==

Heat feedback supports evaporation and pyrolysis, supplying gaseous fuel to flames. Flames then release more energy and can increase feedback. This loop can sustain combustion, accelerate spread or decline depending on the balance between incoming heat and losses.<ref name="Beyler-Hirschler-1-110" /><ref name="VR-4.3" />

[[Fire spread]] occurs when heat transfer enables combustion to extend to new fuel or new locations. Direct flame contact, convective heating, radiation and conduction through boundaries can each contribute. The route and distance affect both timing and the conditions required for ignition.<ref name="VR-5.3" /><ref name="IFEG-2.6">Australian Building Codes Board et al. (2005), pp. 2.6-2, 2.6-6.</ref>

Within a compartment, hot gases collect near the ceiling and transfer energy to boundaries and contents. Radiation from flames, hot gases and heated surfaces can preheat other fuel. Conduction through walls and ceilings can expose the unexposed side even without smoke passing through.<ref name="VR-5.2" /><ref name="VR-5.4" />

[[Fire dynamics]] brings these processes together with fuel production, combustion, buoyancy and ventilation. Heat release rate influences plume flow and gas temperature, while the resulting heat transfer changes fuel response and heat release rate. This feedback prevents a fire from being understood as a fixed heat source isolated from its surroundings.<ref name="IFEG-2.5-2">Australian Building Codes Board et al. (2005), p. 2.5-2.</ref><ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

Scale changes the relative pathways. Reduced-scale experiments can misrepresent radiation because the proportion of radiative transfer changes with flame size. Tien and colleagues report radiation as dominant in flames with characteristic lengths above 0.2 m in the discussed fire context, while convection is more significant in smaller flames. This is a broad source observation, not a universal boundary for every flame.<ref name="Tien-1-73" />

== Engineering applications ==

Heat-transfer analysis supports estimates of ignition exposure, gas temperature, structural heating and conditions at the unexposed side of a barrier. The output should match the decision: heat flux for exposure, internal temperature for material response or transported power for smoke and energy flow.<ref name="VR-5.1" /><ref name="IFEG-2.6" />

For a wall, a steady layered-resistance method can compare constructions under selected boundary temperatures. For changing fires, transient calculations track energy storage and internal gradients. Direction-dependent properties and parallel paths through framing can require more detailed geometry.<ref name="VR-5.2" /><ref name="Rockett-Milke-1-28">Rockett and Milke (2002), p. 1-28.</ref><ref name="Rockett-Milke-1-31">Rockett and Milke (2002), p. 1-31.</ref>

For smoke, plume methods estimate how much air and energy rise from the fire. Surface convection methods then address heat delivered to ceilings or devices. These models share inputs but are not interchangeable, because transported energy and local surface heat flux answer different questions.<ref name="VR-5.3" /><ref name="IFEG-2.5-2" />

For radiation, geometry determines how much emitted energy reaches a receiver. Surface orientation, separation, emissivity and participating gases or soot can all matter. A source temperature alone therefore cannot define the heat flux at another object.<ref name="Tien-1-75" /><ref name="VR-5.4" />

== Source, path and receiver ==

A useful heat-transfer description identifies a source, a path and a receiver. The source may be a flame, hot gas layer or heated surface. The path can include radiation through gas, convection along a surface and conduction through a solid. The receiver can be fuel, a construction, a person or a device.<ref name="VR-5.1" /><ref name="Tien-1-75" />

This separation prevents source heat release from being confused with receiver exposure. Not all energy released by combustion reaches one object, and energy arriving there can be reflected, absorbed, stored or transmitted onwards. Receiver heat flux is therefore a result of the whole configuration.<ref name="Tien-1-73" /><ref name="Rockett-Milke-1-29" />

The receiver's initial condition also matters. Its temperature, moisture and material properties influence how much energy is required for heating and how deeply that heating penetrates. Two receivers at the same location can consequently follow different temperature histories.<ref name="Rockett-Milke-1-29" />

Paths can change as the fire develops. Rising smoke can reach a ceiling and spread horizontally, new surfaces can become hot radiators, and increasing solid temperatures can reduce subsequent heat absorption. A model with one fixed pathway may therefore apply only to a limited stage.<ref name="VR-5.3" /><ref name="VR-5.4" />

Time provides the final connection between these elements. A large heat flux for a short period and a smaller flux for a long period do not automatically produce the same result. Thermal storage, decomposition and changing boundary conditions make the sequence of exposure important.<ref name="VR-5.1" /><ref name="Rockett-Milke-1-29" />

== Selecting models and data ==

Model selection begins with the required output and timescale. A steady resistance model can compare heat flow under fixed boundary temperatures, while a transient model is needed for temperature development during growth and decay. Choosing the simpler model does not remove the need to test its assumptions.<ref name="VR-5.1" />

Scale deserves particular attention in experiments. Tien and colleagues explain that reduced fire scales can reduce the proportion of radiation compared with other mechanisms. A small test can therefore represent convective behaviour more strongly than the full-scale fire it is intended to inform.<ref name="Tien-1-73" />

Material data should match the expected temperature range and direction of transfer. Conductivity, specific heat and emissivity can vary, and composite materials may not behave identically in every direction. Using one ambient value throughout a severe exposure is an assumption, not a property of every material.<ref name="Rockett-Milke-1-28" /><ref name="VR-5.4" />

Geometry enters through several routes. Conductive area and thickness, convective orientation and boundary layers, and radiative view between surfaces all affect the result. Precise material properties cannot compensate for an incorrect physical arrangement.<ref name="VR-5.2" /><ref name="Atreya-1-44" /><ref name="Tien-1-75" />

== Limits and common misunderstandings ==

Heat and temperature are not the same quantity. Temperature describes thermal state, while heat transfer is energy movement caused by temperature difference. A small hot source can transfer little total energy, and a large flow at a lower temperature can transport substantial power.<ref name="VR-5.3" /><ref name="Drysdale-1-91">Drysdale (2002), p. 1-91.</ref>

No mechanism is always dominant. Temperature, scale, geometry and material properties can shift the balance between conduction, convection and radiation. The 70% convection and 30% radiation rule of thumb should not replace an assessment of these conditions.<ref name="VR-4.3" /><ref name="Tien-1-73" />

An intact barrier does not necessarily prevent thermal exposure. Conduction can heat its unexposed surface, which then transfers heat to its surroundings. Evaluating only flame or smoke penetration misses this pathway through the solid.<ref name="VR-5.2" /><ref name="IFEG-2.6" />

Heat transfer can also limit fire growth. Heat losses can suppress ignition and extinguish combustion, while controlled removal can reduce structural and occupant exposure. The engineering question is where the energy goes, at what rate and with what effect over time.<ref name="Drysdale-1-97" /><ref name="VR-5.1" />

Peak heat flux and accumulated energy describe different aspects of exposure. A short peak may occur before a thick section has responded fully, while prolonged moderate heating can raise deeper temperatures. The assessment period should therefore match the failure or ignition mechanism being considered.<ref name="Rockett-Milke-1-29" /><ref name="VR-5.1" />

Contributions can be combined only on a consistent basis. Radiative and convective fluxes must refer to the same receiving surface and period, and conductive loss must use the corresponding solid boundary. Mixing instantaneous values from different fire stages would not form a valid energy balance.<ref name="VR-5.3" /><ref name="Tien-1-75" />

== Notes ==

<references />

== References ==

* Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
* Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-73–1-89). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Physics & Heat Transfer]]

Smouldering

2026-11-02T17:36:00Z

Peter: Improve FSE wiki article: Smouldering; source, clarity and calculation review (GPT-6)

'''Smouldering''' is slow, relatively low-temperature and flameless [[Combustion]] sustained by heat released when oxygen reacts directly with a fuel surface. The reaction occurs on the material itself, unlike a flame in which gaseous fuel reacts. It commonly occurs in porous, char-forming materials and can spread within a fuel bed with little external sign. This can significantly delay recognition.<ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

The process presents two principal fire hazards. It can convert a relatively large proportion of fuel into toxic compounds, although more slowly than many flaming fires. It can also provide a pathway to flaming from an initial heat source too weak to ignite a flame directly. These hazards can develop over long periods and in concealed locations.<ref name="Ohlemiller-2-200" />

Smouldering should not be confused with smoke produced by forced thermal decomposition. [[Pyrolysis]] can gasify an organic material with little or no oxidation, whereas smouldering requires surface oxidation. The presence of smoke alone therefore does not establish which process is occurring. Assessment has to address hidden reaction zones, accumulated exposure, fuel-bed geometry and possible later flaming, rather than relying on visible flame or one universal spread rate for every material and airflow condition.<ref name="Ohlemiller-2-200" /><ref name="Ohlemiller-2-209">Ohlemiller (2002), p. 2-209.</ref>

== Conditions that sustain smouldering ==

Finely divided fuel provides a large surface area per unit mass, which facilitates oxygen attack. A permeable aggregate allows oxygen to reach the reaction zone by diffusion and convection. If the aggregate also resists heat loss, the limited energy released by surface oxidation can maintain the reaction.<ref name="Ohlemiller-2-200" />

Char formation is central for many cellulosic fuels. Char is typically richer in carbon and has greater surface area per unit mass than the original material. Oxygen can react with this porous residue to produce mainly carbon monoxide and carbon dioxide, supplying much of the heat for sustained smoulder propagation.<ref name="Ohlemiller-2-200" />

A burning cigarette combines several favourable features: finely divided fuel, a permeable structure and thermal insulation. It can also initiate smouldering in upholstery and bedding. These composite products involve both fabric and filling, so their combined response can differ from either material tested alone.<ref name="Ohlemiller-2-200" /><ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref>

The conditions needed to initiate smouldering are not necessarily sufficient for it to spread away from the initiation region. Continued propagation depends on heat generation, oxygen transport and heat transfer to adjacent fuel. The factors controlling a later transition to flaming are different again.<ref name="Ohlemiller-2-200" />

[[Self-heating]] can contribute to the initial temperature rise when oxidation within a material releases energy faster than it is lost. Fuel size and shape influence this balance by changing heat retention. Self-heating describes energy accumulation, while smouldering describes the sustained surface-combustion process that can follow under suitable conditions.<ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref>

== Propagation and oxygen supply ==

After initiation, the smouldering zone often consumes oxygen as quickly as it reaches the reaction region. Propagation is then strongly controlled by oxygen transport. Thick fuel layers slow oxygen delivery but also retain heat, allowing very slow reaction zones to persist.<ref name="Ohlemiller-2-201">Ohlemiller (2002), p. 2-201.</ref>

In reverse smouldering, oxygen moves opposite to the direction of front propagation. It can reach the reaction zone by diffusion or by forced airflow through unburnt fuel. In forward smouldering, oxygen and the front move in the same general direction. These relative directions change preheating, heat retention and product composition.<ref name="Ohlemiller-2-201" /><ref name="Ohlemiller-2-203">Ohlemiller (2002), p. 2-203.</ref>
[[File:fse-smouldering-v1.svg|thumb|upright=1.5|alt=Two fuel beds with opposite and matching oxygen-flow and front-direction arrows.|Forward and reverse smouldering differ in relative oxygen-flow direction. Based on Ohlemiller (2002), pp. 2-201–2-203.]]

Ohlemiller describes sawdust experiments in which smouldering took about two weeks to move upwards through a layer 1 m deep. In another set of reverse-smoulder experiments, velocities were of the order of 0.0001 m/s across several fuels under the stated airflow conditions. These results illustrate possible timescales but do not provide a universal smouldering speed.<ref name="Ohlemiller-2-201" /><ref name="Ohlemiller-2-202">Ohlemiller (2002), p. 2-202.</ref>

The diffusion-controlled sawdust case has a useful scaling relation. As the front advances through unburnt fuel towards the surface, the distance through which oxygen must travel changes. Ohlemiller reports that the penetration time is approximately proportional to the square of the layer depth. The proportionality constant must be obtained from a measurement on the fuel configuration being considered:<ref name="Ohlemiller-2-202" />

<math display="block">t_L=A L^2</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>t_L</math> || Time for the front to penetrate the fuel layer || s
|-
| <math>L</math> || Layer depth || m
|-
| <math>A</math> || Empirical coefficient fitted to the same fuel and oxygen-supply conditions || s/m²
|}

For an illustrative scaling calculation, represent the reported two weeks at 1 m as 14 days. Keeping the same coefficient, a layer half as deep gives one quarter of that penetration time: 3.5 days. The result follows from the source's square-law model, rather than from a separate test of that shallower layer:<ref name="Ohlemiller-2-201" /><ref name="Ohlemiller-2-202" />

<math display="block">t_{0.5\,\mathrm{m}}=14\left(\frac{0.5}{1.0}\right)^2=3.5\ \mathrm{days}</math>

This estimate applies to approximately one-dimensional, diffusion-dominated propagation under comparable conditions. A non-uniform deposit can contain easier airflow paths, and buoyancy can introduce convection through the fuel. The fitted constant and square-law assumption cannot then be transferred automatically. The calculation illustrates the importance of oxygen transport and depth; it does not predict an incident's duration or extinction time.<ref name="Ohlemiller-2-202" />

Deep reaction zones can remain hidden until they approach a free surface. Oxygen access increases near that surface, while buoyancy and local airflow change heat and mass transfer. A fire can consequently show little sign internally before becoming more obvious at the exterior.<ref name="Ohlemiller-2-202" />

Real fuel beds often have two- or three-dimensional temperature and composition gradients. The upper part of a horizontal layer usually receives oxygen more readily than deeper material, producing an inclined reaction zone. Simple one-dimensional descriptions therefore apply only to selected configurations.<ref name="Ohlemiller-2-204">Ohlemiller (2002), p. 2-204.</ref>

== Heat loss, airflow and fuel-bed size ==

A self-sustaining reaction requires heat generation to keep pace with heat loss. Thin layers have a large surface relative to their volume and can lose energy too rapidly. Below a minimum thickness, smouldering therefore stops. That thickness depends on fuel type, particle size, bulk density and oxygen supply.<ref name="Ohlemiller-2-205">Ohlemiller (2002), p. 2-205.</ref>
[[File:fse-smouldering-v2.svg|thumb|upright=1.5|alt=Thin layer losing heat and thick layer retaining heat around a slow reaction zone.|Fuel-bed thickness affects the heat balance for sustained smouldering. Based on Ohlemiller (2002), pp. 2-201–2-205.]]

Airflow can either strengthen or weaken the process. Increased oxygen supply can raise heat release and accelerate spread, but sufficiently strong flow can add cooling and disrupt the reaction zone. The response depends on flow direction, fuel-bed geometry and whether propagation is forward or reverse.<ref name="Ohlemiller-2-205" />

Fuel particle size affects more than chemical surface area. It changes permeability, insulation and the minimum layer depth needed for sustained spread. In the sawdust and cork experiments described by Ohlemiller, particle size had less influence on velocity than flow configuration, but it strongly affected limiting thickness.<ref name="Ohlemiller-2-205" />

Scale can also allow smouldering to pass beneath an intended barrier. In laboratory studies of deep fuel beds, heated and partly decomposed material below an initial reaction zone supported a second wave moving in the opposite direction. Ohlemiller warns that inert covering layers may slow rather than stop such fires.<ref name="Ohlemiller-2-206" />

== Smoke, carbon monoxide and detection ==

Smouldering can produce substantial [[Carbon monoxide]] relative to the fuel converted. The yield and concentration vary with fuel and airflow, so a single value cannot represent all smouldering fires. The slow release rate does not remove the hazard because exposure can accumulate over a long period in an enclosure.<ref name="Ohlemiller-2-200" /><ref name="Ohlemiller-2-202" />

In one flexible-polyurethane-foam experiment, carbon monoxide comprised 6% to 7% of evolved gases on a molar basis at an imposed air velocity of 0.0015 m/s. Cellulosic insulation in another test varied from about 10% to 22% as airflow changed. These are configuration-specific measurements, not safe-exposure criteria or universal material yields.<ref name="Ohlemiller-2-202" />

The aerosol from smouldering differs from sooty flaming smoke. For the cellulosic-insulation source studied by Ohlemiller, the mass mean particle size was 2 to 3 micrometres, larger than cigarette smoke and much larger than particles from the flaming source used for comparison. The fuel bed also filtered part of the aerosol before it escaped.<ref name="Ohlemiller-2-203" />

This behaviour affects [[Smoke detector]] response. Ohlemiller links the large aerosol particles with relatively poor sensitivity of ionisation detectors to the realistic smouldering source examined. Deep smouldering may also remain undetectable until it nears an exposed surface because the fuel bed traps products.<ref name="Ohlemiller-2-203" />

The weak heat source presents a further detection problem. Reverse-smoulder sources discussed in the handbook produced only a few hundredths of a kilowatt in the stated configurations. Their buoyant plumes might not reach the ceiling of a room, limiting the transport of combustion products to ceiling-mounted devices.<ref name="Ohlemiller-2-203" />

== Transition to flaming ==

[[Smouldering-to-flaming transition]] requires a flammable mixture of pyrolysis gases and air and sufficient heat to ignite it at the same place and time. Increased oxygen supply, larger scale and reduced heat losses can promote both conditions. The transition is therefore possible but not inevitable.<ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

Forward smouldering can be particularly favourable in some fuel beds because heat transfer intensifies the reaction near its leading edge. Cavities formed there can collect fuel gases and stabilise initial flames. Different materials and configurations produce other mechanisms, so there is no single transition temperature or airflow for all smouldering fires.<ref name="Ohlemiller-2-208" />

Experiments with upholstered furniture demonstrate the wide time range. In a survey cited by Ohlemiller, about two thirds of tested chairs and beds made the transition, with reported times from 22 to 306 minutes after smouldering began. These results describe the tested objects and should not be used as a countdown for an actual incident.<ref name="Ohlemiller-2-208" />
[[File:fse-smouldering-v3.svg|thumb|upright=1.5|alt=Observed range from 22 to 306 minutes for tested chairs and beds.|Reported smouldering-to-flaming times in a furniture-test survey. Based on Ohlemiller (2002), p. 2-208.]]

Neighbouring materials can change the outcome. Retardants that prevented transition in an isolated cellulosic insulation layer became less effective when that layer touched unretarded wood. Heat from the smouldering zone could ignite the adjacent material even when the original fuel did not flame.<ref name="Ohlemiller-2-208" />

== Detection, extinction and reignition ==

Effective extinction requires more than suppressing visible glow. Oxygen exclusion can stop reaction temporarily, but oxygen readmission can cause reignition while the fuel remains hot. Ohlemiller states that oxygen removal may have to continue until cooling is sufficient, and that obtaining this cooling can be exceptionally difficult in a large porous bed.<ref name="Ohlemiller-2-206" />

Extinguishing agents can also miss concealed reaction zones. In grain silos, higher-permeability channels can allow an agent to bypass significant smouldering regions. Emptying before complete extinction introduces another hazard because combustible dust can become dispersed. The source treats this as a practical configuration problem rather than a simple choice of agent.<ref name="Ohlemiller-2-207">Ohlemiller (2002), p. 2-207.</ref>

Assessment after an intervention therefore includes the temperature and location of remaining fuel, not only the atmosphere above it. A deep bed can retain reactive material for long periods. Restored airflow can then change both oxygen supply and heat loss, with outcomes that depend on the new conditions.<ref name="Ohlemiller-2-205" /><ref name="Ohlemiller-2-206" />

== Buildings and outdoor fuel beds ==

Upholstery and bedding combine fabrics, fillings and crevices, producing behaviour that a single-material specimen may not reproduce. A cellulosic fabric can supply heat to polyurethane foam while both compete for oxygen. Ohlemiller reports that this combination can smoulder over a wider range of conditions than the foam alone.<ref name="Ohlemiller-2-206" />

Closed-room mattress experiments show why slow development still requires attention. In two of five cigarette-initiated cotton-mattress tests described in the handbook, flaming followed smouldering after 65 to 80 minutes. In other bedding and upholstery tests, flaming usually required two to three hours of prior smouldering. These observations belong to the tested products and rooms, and are not general predictions.<ref name="Ohlemiller-2-206" />

Solid wood presents a different configuration from loose fibres. Its lower permeability limits oxygen access to the decomposition region, and a single layer may lose too much heat to sustain smouldering without additional exposure. Ohlemiller reports a requirement of about 10 kW/m² of external heat input in the cited solid-wood configuration. Other wood forms and arrangements can behave differently.<ref name="Ohlemiller-2-204" />

Peat and organic material on a forest floor can retain smouldering after a flaming front has passed. The process is spatially irregular and can later support renewed flaming. This outdoor example involves a porous fuel bed with oxygen entering largely from above, rather than a manufactured uniform specimen.<ref name="Ohlemiller-2-206" />

== Engineering use and uncertainty ==

Design-fire descriptions sometimes include a smouldering phase. The 2005 International Fire Engineering Guidelines distinguish smouldering fires that remain flameless from those that later become flaming. The transition remains difficult to predict from fuel identity alone because airflow, geometry and heat losses affect its onset.<ref name="IFEG-1.2-29">Australian Building Codes Board et al. (2005), p. 1.2-29.</ref><ref name="Ohlemiller-2-208" />

The same older guidelines use a notional maximum heat release rate below 5 kW for an illustrated smouldering design fire. This is a modelling choice in that guidance, not a universal physical maximum. Experimental source strengths and spread rates need to be tied to the fuel bed and airflow from which they were obtained.<ref name="IFEG-1.2-29" /><ref name="Ohlemiller-2-203" />

Ohlemiller concludes that quantitative guidance for realistic smoulder propagation, detection, toxic production and transition remains limited. Experimental results can support closely analogous situations, but dissimilar materials and geometries require caution. Fuel chemistry alone is not enough to predict spread when oxygen transport and heat retention dominate.<ref name="Ohlemiller-2-209" />

Toxic assessment needs the material and combustion mode as well as carbon monoxide. The 2005 guidelines identify carbon monoxide as the principal toxic species for many fires, but caution that atypical materials require broader analysis. They specifically note that smouldering polyurethane foam can yield significant hydrogen cyanide.<ref name="IFEG-2.4-12">Australian Building Codes Board et al. (2005), p. 2.4-12.</ref>

Source terms should therefore be based on appropriate experimental data for the combustible and the smouldering condition. A flaming-fire yield cannot be substituted automatically, and a slow source can continue for much longer than the test used to characterise it. Both yield and duration influence the exposure calculated for an enclosure.<ref name="IFEG-2.4-12" /><ref name="Ohlemiller-2-209" />

== See also ==

* [[Fire development stages]]
* [[Firebrands]]
* [[Hot work]]
* [[Mass timber]]
* [[Timber in fire]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.

[[Category:Combustion]]

Fire spread

2026-11-02T17:34:45Z

Peter: Improve FSE wiki article: Fire spread; source, clarity and calculation review (GPT-6)

'''Fire spread''' is the extension of combustion from its initial location to additional fuel, spaces or structures. It can occur as continuous flame movement, successive ignition of separate objects, heat transfer through a barrier, burning debris carried to a new location or a combination of these routes. The process links ignition with fire growth beyond the first burning item.<ref name="Kanury-2-229">Kanury (2002), p. 2-229.</ref><ref name="IFEG-1.6-7">Australian Building Codes Board et al. (2005), p. 1.6-7.</ref>

Spread changes both the size and the location of the fire. Additional fuel can increase heat release rate, while new openings and spaces can alter ventilation and smoke movement. A developing fire therefore cannot be assessed only from its initial source and fuel package.<ref name="IFEG-1.6-3">Australian Building Codes Board et al. (2005), pp. 1.6-3–1.6-5.</ref><ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

The relevant scale ranges from millimetres across a surface to flames and brands travelling between buildings. Each scale has different controlling heat-transfer and ignition conditions. Spread rate and direction are consequently scenario properties rather than fixed material constants.<ref name="Quintiere-2-246">Quintiere (2002), p. 2-246.</ref><ref name="IFEG-2.6-12">Australian Building Codes Board et al. (2005), p. 2.6-12.</ref>

== Successive ignition and heat transfer ==

Kanury describes fire spread over combustibles as continuous ignition of successive upstream material. The existing fire heats fuel ahead of the burning region until that fuel reaches its own ignition condition. Fuel production, mixing and heat loss at the new location all influence the time required.<ref name="Kanury-2-229" /><ref name="Kanury-2-230">Kanury (2002), p. 2-230.</ref>

Direct flame contact supplies intense local heating and a pilot. Radiation can act across a gap without flame or smoke touching the target, while convection carries hot gases to remote surfaces. Conduction transmits energy through solids, including walls and structural boundaries.<ref name="VR-5.1">Van Rossum (2027), §5.1.</ref><ref name="IFEG-1.6-7" />
[[File:fse-fire-spread-v1.svg|thumb|upright=1.5|alt=Fire reaching new fuel through flames, radiation, a wall and flying embers.|Four fire-spread pathways to new fuel. Based on Australian Building Codes Board et al. (2005), p. 1.6-7.]]

The target's arrangement affects each route. Thin or light items can respond quickly, while thick items can absorb energy internally. Orientation changes convective flow and the area exposed to flame radiation, and nearby surfaces can provide shielding or additional reflected and emitted energy.<ref name="Quintiere-2-247">Quintiere (2002), p. 2-247.</ref><ref name="Tien-1-75">Tien, Lee, and Stretton (2002), p. 1-75.</ref>

Heat received by a target is not equal to total fire heat release. Only part reaches the object, and that part is balanced against losses and storage. Spread analysis therefore requires source exposure, target ignition response and time, not just the size of the original fire.<ref name="Rockett-Milke-1-29">Rockett and Milke (2002), p. 1-29.</ref><ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

== Flame spread over continuous fuel ==

[[Flame spread]] over a solid or liquid involves a moving gas-phase flame close to the condensed fuel that supplies its vapour. Quintiere distinguishes the visible flame front from the evaporation or pyrolysis front in the fuel. The movement of the latter defines surface flame-spread velocity.<ref name="Quintiere-2-246" />

The flame must heat material ahead of itself for spread to continue. If that heating is too weak or heat losses are too large, the front can slow or stop. If preheating is strong, spread can accelerate as more fuel becomes involved.<ref name="Quintiere-2-247" />

Direction matters because fire-induced flow changes with orientation. Upward spread can preheat a large region above the flame, whereas lateral or downward spread relies on different forward heat-transfer paths. Opposed and wind-aided flow can therefore produce very different rates on the same material.<ref name="Quintiere-2-247" /><ref name="VR-4.3">Van Rossum (2027), §4.3.</ref>

Spread over a continuous surface differs from flame propagation through a premixed gas cloud. In the latter, fuel and oxidiser are already distributed in the gas phase. Surface spread instead requires continuing evaporation or decomposition at the condensed-fuel boundary.<ref name="Quintiere-2-246" />

== Spread between separate objects ==

Separate objects introduce gaps across which heat must travel. Flame contact, radiation and burning debris can bridge these gaps, while convective flow can expose objects farther away. The time of each new ignition determines the spatial development of the overall fire.<ref name="IFEG-1.6-7" /><ref name="IFEG-2.4-4" />

The 2005 International Fire Engineering Guidelines describe a simplified pre-flashover method for radiant ignition of a second item. It neglects radiation from the upper layer and room surfaces and uses flame radiation from the first item. This assumption belongs to that stage and method, and is unsuitable for a developed hot compartment.<ref name="IFEG-2.4-4" />

[[Fire spread between buildings]] can involve radiation through closed or fixed windows, direct flame contact and burning debris. The guidelines note that radiation can pass through glass without glass breaking. If breakage occurs, it can create both a new spread route and a ventilation change.<ref name="IFEG-1.6-7" />

[[Firebrands]] and embers add discontinuous spread. Burning material can rise in a thermal plume and be carried by wind before igniting a remote target. The 2005 guidelines caution that travel distance is difficult to establish with certainty, so precise brand trajectories should not be invented.<ref name="IFEG-2.6-12" />

== Barriers and compartmentation ==

[[Fire compartmentation]] divides a building into enclosures intended to limit fire and smoke spread. Its effectiveness depends on barriers, openings, firestopping, structural stability and the combustibles on both sides. An assessment therefore considers failure modes as well as nominal fire resistance.<ref name="IFEG-1.6-3" /><ref name="IFEG-1.6-7" />

Conductive failure can occur when enough heat passes through a barrier to meet a failure criterion, even without loss of integrity or stability. Combustibles in the next enclosure can then be exposed on the unexposed side. The barrier can remain physically intact while this thermal pathway develops.<ref name="IFEG-1.6-7" />
[[File:fse-fire-spread-v2.svg|thumb|upright=1.5|alt=Three panels: heat through intact wall, cracked barrier and collapsed barrier.|Barrier failure can be thermal, integrity-related or structural. Based on Australian Building Codes Board et al. (2005), p. 1.6-7.]]

Loss of integrity involves cracks, fissures or failure of firestopping. Hot gases, flames and radiation can then reach adjacent fuel through paths that were previously limited. The timing of such failure can also change smoke movement and ventilation.<ref name="IFEG-1.6-7" />

Loss of stability involves collapse of the barrier, whether or not it is a structural element. This can create a large opening and expose new areas to flames and radiation. Structural failure and integrity failure are therefore distinct events in spread analysis.<ref name="IFEG-1.6-7" />

A barrier can also depend on other structural elements for support. Failure of a supporting member may cause the barrier to fail before its own thermal resistance is exhausted. The IFEG consequently requires the structural sequence and its consequences for dependent barriers to be considered together.<ref name="IFEG-1.6-8">Australian Building Codes Board et al. (2005), p. 1.6-8.</ref>

Doors and windows introduce time-dependent opening states. The guidelines suggest obtaining door-opening times from evacuation analysis and evaluating glass breakage from fire severity. These changes connect occupant movement and component response with the fire's ventilation and spread path.<ref name="IFEG-1.6-7" />

== Compartment fire and flashover ==

Within a compartment, flames, hot gases and heated boundaries preheat additional fuel. As more objects ignite, heat release rate and gas temperature can increase, producing stronger feedback. Spread is therefore coupled with the compartment energy balance rather than being a simple sequence of independent objects.<ref name="VR-4.3" /><ref name="Drysdale-1-95" />

[[Flashover]] represents a transition towards widespread involvement of combustible surfaces in the compartment. It can follow successive ignition and radiative preheating, but its timing depends on the complete enclosure and ventilation scenario. Spread before flashover requires assumptions appropriate to that stage.<ref name="IFEG-2.4-4" /><ref name="VR-4.7">Van Rossum (2027), §4.7.</ref>

After widespread involvement, unburnt volatiles can leave the compartment and burn outside after mixing with air. This external flaming can expose upper facades and neighbouring surfaces. The location of heat release consequently extends beyond the original fuel and room.<ref name="Drysdale-1-95" />

[[Facade fire]] introduces exterior surfaces, cavities and cladding arrangements into the spread problem. The 2005 guidelines include concealed spaces behind exterior cladding and flames projecting through windows among possible paths. These arrangements require their own geometry and material assessment rather than a room-only model.<ref name="IFEG-1.6-6">Australian Building Codes Board et al. (2005), pp. 1.6-6–1.6-7.</ref>

== Large spaces and travelling involvement ==

Large open-plan enclosures make simultaneous burning of the whole floor unrealistic in many scenarios. Travel time between fuel packages becomes significant relative to the duration of a localised fire. Assuming the entire area burns at once can produce unrealistically high temperatures.<ref name="IFEG-2.6-12" />

The 2005 guidelines describe a grid approximation for large enclosures, using time offsets as fire moves between grid areas. Where object locations and ignition criteria are known, spatial development can instead be based on individual items. Both methods require defensible fuel arrangement and spread timing.<ref name="IFEG-2.6-12" />
[[File:fse-fire-spread-v3.svg|thumb|upright=1.5|alt=Large floor grid with fire moving between regions at different times.|Grid time offsets represent spread across a large enclosure. Based on Australian Building Codes Board et al. (2005), p. 2.6-12.]]

The suggested grid areas are 10–50 m² in the 2005 method. Each region contributes its heat release after the assigned spread delay. The grid therefore represents a sequence of involvement; it does not calculate the delay from ignition physics. Using individual objects can improve the representation when their type and location remain predictable throughout the building's life.<ref name="IFEG-2.6-12" />

Vertical shafts and concealed spaces extend the relevant enclosure beyond the room of origin. Flame and hot gas can reach other floors through these routes. Analysis limited to horizontal spread across one floor would miss them.<ref name="IFEG-1.6-7" />

Fire spread can also alter suppression and evacuation conditions. New ignition locations change detection, available escape time and the area requiring intervention. The guidelines use spread and barrier-failure times as inputs to these wider assessments.<ref name="IFEG-1.6-3" />

== Rates, acceleration and extinction ==

Spread accelerates when newly involved fuel increases heat release and preheating faster than losses and fuel depletion limit them. Quintiere compares spread time with burn time: rapid spread relative to burning can accelerate growth, while slow spread can allow the original fuel to burn out before new ignition occurs.<ref name="Quintiere-2-246" />

The process is therefore unstable rather than inherently steady. A small change in heat flux, initial temperature or fuel arrangement can shift the balance towards acceleration or extinction. Initial temperatures closer to the ignition condition reduce additional heating required ahead of the front.<ref name="Quintiere-2-247" />

Representative rates illustrate scale rather than universal values. Quintiere gives lateral or downward spread on thick solids as roughly 0.1 cm/s in order of magnitude, compared with 1 to 100 cm/s for upward spread and several other phenomena. These ranges from the 2002 handbook should not be assigned to an untested material without matching conditions.<ref name="Quintiere-2-247" />

Spread can stop when heat transfer ahead of the flame becomes insufficient, fuel becomes discontinuous or oxygen and combustion conditions no longer support propagation. Fire growth is therefore not inevitable even after a substantial initial fire.<ref name="Quintiere-2-246" /><ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref>

== Assessment and radiation calculations ==

A spread assessment should identify the first item, potential targets, heat-transfer routes and barrier states. It then needs timing for each new ignition or failure and the corresponding changes in heat release and ventilation. This structure makes the assumed path explicit.<ref name="IFEG-1.6-3" />

Source and target data must share compatible conditions. Flame-spread tests, ignition tests and barrier tests answer different questions, and their results cannot be substituted without a model. Geometry and scale should remain visible throughout.<ref name="Quintiere-2-247" /><ref name="IFEG-1.6-7" />

Firebrand travel and large-space spread carry particular uncertainty. Precise distances and simultaneous involvement should not be asserted without supporting evidence. Sensitivity to target location and ignition timing can show whether the overall conclusion changes.<ref name="IFEG-2.6-12" />

A simplified radiation calculation illustrates one link in the spread sequence. The IFEG represents a luminous flame as a radiating panel with a uniform effective temperature and emissivity. A configuration factor describes how the target's position and orientation relate to that panel. Multiplying these terms gives the radiation incident at the target.<ref name="IFEG-2.4-7">Australian Building Codes Board et al. (2005), pp. 2.4-7–2.4-9.</ref>

<math display="block">q_r=\phi\sigma\varepsilon T_f^4</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>q_r</math> || Incident radiant heat flux at the target || W/m²
|-
| <math>\phi</math> || Configuration factor for the radiating panel and receiving point || Dimensionless
|-
| <math>\sigma</math> || Stefan–Boltzmann constant, 5.68 × 10⁻⁸ in the cited IFEG equation || W/(m²·K⁴)
|-
| <math>\varepsilon</math> || Effective emissivity of the source || Dimensionless
|-
| <math>T_f</math> || Effective source temperature || K
|}

The temperature must be entered in kelvin because the equation contains its fourth power. The configuration factor is geometric; it accounts for the visible panel size, separation and orientation. An obstruction or a different receiving position can change the exposure. This is why fire temperature alone cannot establish the heat flux reaching another object.<ref name="IFEG-2.4-7" /><ref name="Tien-1-75" />

For an illustrative calculation, choose a source temperature of 1,000 K and a configuration factor of 0.10. The IFEG permits an emissivity of 1.0 as a conservative assumption for thick luminous flames. The chosen temperature and factor are example inputs, not measurements of a particular fire. Using the constant printed in the 2005 guidelines gives approximately 5.7 kW/m².<ref name="IFEG-2.4-7" />

<math display="block">q_r=0.10\times(5.68\times10^{-8})\times1.0\times1000^4=5680\;\mathrm{W/m^2}\approx5.7\;\mathrm{kW/m^2}</math>

If geometry reduces the configuration factor to 0.05, with the other assumptions unchanged, the calculated exposure falls to about 2.8 kW/m². This demonstrates the effect of geometric separation and orientation through the factor. It does not determine a specific separation distance, which would require the actual panel dimensions and target position.<ref name="IFEG-2.4-7" />

The result is incident radiation from the represented source. It is not the target's net heat gain or proof that ignition occurs. Target absorption, heat losses, internal heating and exposure duration still determine its thermal response. Kanury's ignition analysis also requires sufficient combustible gas production, mixing with oxygen and a suitable ignition condition.<ref name="Rockett-Milke-1-29" /><ref name="Kanury-2-230" /><ref name="Kanury-2-232">Kanury (2002), p. 2-232.</ref>

The uniform panel is a simplification of the flame's changing shape and temperature. The guidelines also discuss point-source and cylindrical-flame methods, each with its own assumptions. A point-source screening model uses an inverse-square relationship, whereas a panel model explicitly represents the emitting geometry. Their results cannot be combined without retaining those different representations.<ref name="IFEG-2.4-7" />

Radiation across intact glazing requires further care. The possibility of transmission does not mean the glass transmits all incident radiation. Glass breakage can subsequently create a different exposure and alter the compartment's ventilation. The IFEG therefore treats the initial radiation path and the later opening event separately in its fire-spread sequence.<ref name="IFEG-1.6-7" />

Likewise, a barrier reaching an assumed failure criterion does not itself describe the receiving fuel's response. The guidelines allow barrier failure to stand for spread in simplified analyses, but distinguish that assumption from actual ignition. The fuel's ignitability and arrangement on the receiving side remain relevant. This distinction makes the scope of a calculated spread time explicit.<ref name="IFEG-1.6-7" />

== See also ==

* [[Car park fire]]
* [[Cavity barrier]]
* [[Heat transfer]]
* [[Wildfire]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Kanury, A. M. (2002). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-229–2-245). National Fire Protection Association.
* Quintiere, J. G. (2002). Surface flame spread. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-246–2-257). National Fire Protection Association.
* Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
* Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-73–1-89). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Ignition & Flame Spread]]

Convection

2026-11-02T17:34:27Z

Peter: Improve FSE wiki article: Convection; source, clarity and calculation review (GPT-6)

'''Convection''' is heat transfer associated with the movement of a gas or liquid. In a fire, hot smoke and heated air carry energy as they rise, move through openings or flow along surfaces. Convection also describes the resulting heat exchange between that moving fluid and walls, ceilings, structural members and other objects.<ref name="VR-5.3">Van Rossum (2027), §5.3.</ref>

At a surface, convection combines fluid motion with molecular heat transfer through the adjacent fluid. Radiation can occur alongside it and is calculated separately. Natural movement caused by the fire and forced movement caused by wind or equipment can occur together.<ref name="Atreya-1-44">Atreya (2002), p. 1-44.</ref><ref name="VR-5.3" /><ref name="VR-5.4" />

Convection matters because it can transport heat far beyond the original fuel. It influences fire plumes, ceiling jets, smoke spread, structural heating and the activation of heat-responsive devices. The amount of energy transported and the heat delivered to a particular surface are related but distinct quantities.<ref name="VR-5.3" /><ref name="IFEG-2.5-2">Australian Building Codes Board et al. (2005), p. 2.5-2.</ref>

== Transport by moving gas and liquid ==

A flowing fluid carries its thermal energy with it. Hot combustion products leaving a flame therefore form a moving heat source, not only a cloud of combustion products. As this fluid travels, it can heat objects along its path and transfer energy into other rooms.<ref name="VR-5.3" />

Two descriptions are needed for different engineering questions. The first follows energy carried by a volume or mass flow and gives a rate of energy transport. The second evaluates heat flux from fluid to a surface. Van Rossum notes that these approaches produce different result forms and should not be confused.<ref name="VR-5.3" />

For energy carried by a flow, temperature, density, specific heat capacity and volumetric flow all matter. The temperature difference is taken against a defined reference, such as incoming ambient air. Changing any of these inputs alters the calculated energy transport.<ref name="VR-5.3" />

For surface heating, the temperature difference between gas and surface is combined with a convective heat-transfer coefficient. That coefficient summarises the effect of fluid properties and flow conditions. It is not a universal constant for air, smoke and water, or for every orientation and velocity.<ref name="VR-5.3" /><ref name="Atreya-1-47">Atreya (2002), p. 1-47.</ref>

== Free, forced and mixed convection ==

Free convection occurs when temperature differences create the flow. Hot combustion products have lower density than surrounding cooler air, so [[Buoyancy]] drives them upwards. Cooler air moves into the region and the process continues while heating and density differences persist.<ref name="VR-5.3" /><ref name="Kandola-1-5">Kandola (2002), pp. 1-4–1-5.</ref>
[[File:fse-convection-v1.svg|thumb|upright=1.5|alt=Hot gas rising naturally and a fan forcing gas across a warm surface.|Natural and forced convection use different driving influences. Based on Van Rossum (2027), §5.3.]]

Forced convection is imposed by an external cause such as a fan, pump, wind or mechanical smoke exhaust. These forces can strengthen, redirect or oppose the flow that the fire generates. The resulting pattern depends on their combined influence rather than on one label alone.<ref name="VR-5.3" />

Mixed convection is common in buildings. A hot plume rises naturally while ordinary ventilation, wind at openings or a smoke-control system changes the surrounding pressure field. Even equipment not designed as fire equipment can affect heat and smoke transport.<ref name="VR-5.3" /><ref name="VR-6.6">Van Rossum (2027), §6.6.</ref>

Atreya further distinguishes flows inside bodies, such as pipes, from external flows around objects. Fire assessments commonly emphasise external natural convection around surfaces and within rooms. The chosen geometry determines which measured relationships and boundary conditions are appropriate.<ref name="Atreya-1-44" />

== Fire plumes and ceiling jets ==

A [[Fire plume]] forms as hot gases rise above a fire. Turbulent motion draws surrounding air into this rising stream. The plume's mass flow consequently increases while its temperature and combustion-product concentrations become more diluted.<ref name="VR-5.3" /><ref name="IFEG-2.5-2" />

Entrained air can greatly exceed the mass of burned fuel in the rising flow. The International Fire Engineering Guidelines therefore allow the fuel mass flow to be neglected in particular smoke-development methods. This does not mean the fuel is unimportant; its heat release establishes the buoyant flow that entrains the air.<ref name="IFEG-2.5-2" />

A small fire can consequently produce a much larger flow of warm, diluted smoke. Convective heat transport is not proportional only to the visible flame volume. Air entrainment, plume height and surrounding geometry influence the quantity delivered upwards.<ref name="VR-5.3" />

When the rising flow reaches a ceiling, it turns and spreads horizontally as a [[Ceiling jet]]. This hot, relatively fast-moving layer transfers heat to the ceiling and to objects near it. Flame-zone and ceiling-jet calculations inform evaluations of fire resistance, detectors and sprinklers.<ref name="Alpert-2-18">Alpert (2002), p. 2-18.</ref><ref name="IFEG-2.5-2" />
[[File:fse-convection-v2.svg|thumb|upright=1.5|alt=Rising plume turning sideways into a hot ceiling jet with surface heat transfer.|A plume feeds a convective ceiling jet. Based on Van Rossum (2027), §5.3 and Australian Building Codes Board et al. (2005), p. 2.5-2.]]

As the ceiling jet moves outwards, entrained air dilutes it and heat transfer cools the gases near the ceiling. Accumulation of an upper hot layer changes the surrounding conditions. The initially unconfined ceiling-jet description therefore represents a particular stage of a compartment fire.<ref name="Alpert-2-18" />

== Coefficients, conservation and measurement ==

A convective [[Heat transfer]] coefficient has units of watts per square metre-kelvin when used for surface heat flux. Van Rossum also describes its reciprocal as a surface resistance. A larger coefficient means less resistance under the selected flow model, but it does not provide the total heat flow without area and temperature difference.<ref name="VR-5.3" />

Surface heat flux is calculated by multiplying the gas-to-surface temperature difference by the convective coefficient. If the gas is hotter than the surface, the positive result describes heating of the surface. When the surface becomes hotter than the gas, the sign reverses and convection cools it.<ref name="VR-5.3" /><ref name="Atreya-1-47" />

<math display="block">\dot q''_c=h_c(T_g-T_s),\qquad \dot Q_c=\dot q''_cA</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot q''_c</math> || Convective heat flux into the surface || W/m²
|-
| <math>h_c</math> || Convective heat-transfer coefficient || W/(m²·K)
|-
| <math>T_g,T_s</math> || Gas and surface temperatures || K or °C
|-
| <math>A</math> || Receiving surface area || m²
|-
| <math>\dot Q_c</math> || Total convective heat-transfer rate for uniform flux || W
|}

For a non-uniform exposure, flux can vary across the surface. The total transfer then requires adding the contributions over its area, or using an appropriate average coefficient. A local coefficient from one point does not automatically describe the entire object. Atreya distinguishes these local and area-averaged quantities explicitly.<ref name="Atreya-1-47" />

Van Rossum gives indicative coefficients for several conditions. These are examples of the magnitude of surface transfer, not requirements or constants that apply to every fire. The applicable value depends on the flow at the surface. It also describes convection alone, so radiative exposure needs separate treatment.<ref name="VR-5.2">Van Rossum (2027), §5.2.</ref>

{| class="wikitable"
! Illustrative condition !! <math>h_c</math>, W/(m²·K)
|-
| Ordinary indoor conditions || 1–5
|-
| Smoke layer beneath a roof || 3–10
|-
| Fully developed fire || 20–25
|}

The coefficient summarises processes within the boundary layer rather than a fixed property of the fluid alone. Surface geometry, flow velocity, turbulence and temperature-dependent properties can all influence it. Published coefficients and correlations therefore carry an application range.<ref name="Atreya-1-47" /><ref name="VR-5.3" />

Conservation laws provide the underlying framework. Atreya identifies conservation of mass, momentum and energy, supplemented by relationships for viscosity, conduction and diffusion. For turbulent flow, this framework often guides empirical correlations rather than yielding a simple universal solution.<ref name="Atreya-1-45">Atreya (2002), p. 1-45.</ref>

Measurement must match the intended result. A gas-temperature reading alone does not determine the surface coefficient, and a surface heat-flux reading does not directly give the energy carried through an opening. Flow rate, density and reference temperature are needed for the transported-energy description.<ref name="VR-5.3" />

The density calculation illustrates why units require attention. Van Rossum's exhaust example uses kelvin to determine smoke density, while the temperature difference between smoke and ambient air can be evaluated in degrees Celsius. Confusing these two uses of temperature would change the estimated energy transport.<ref name="VR-5.3" />
[[File:fse-convection-v3.svg|thumb|upright=1.5|alt=Exhaust carries 100 m³/s at 463 °C with ambient 20 °C and result 21.35 MW.|Example of convective power carried by an exhaust flow. Based on Van Rossum (2027), §5.3.]]

== Applying convective analysis ==

Convective transport can ignite light combustible materials at a considerable distance from the original fire. Van Rossum identifies this possibility when hot gases travel through buildings. The receiving material still needs a suitable time-dependent exposure and ignition condition; transport alone does not prove ignition.<ref name="VR-5.3" /><ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

Radiation can act alongside convection along the same path. A surface may receive radiation from a flame or hot gas layer while hot gas flows over it. Calculating only one contribution can underestimate exposure, while adding values based on different reference areas or times can create another error.<ref name="VR-5.4">Van Rossum (2027), §5.4.</ref><ref name="Tien-1-73">Tien, Lee, and Stretton (2002), p. 1-73.</ref>

System operation changes the pressure field and therefore the convective path. Smoke exhaust can remove energy, ordinary ventilation can redistribute it, and wind can alter flow through openings. The analysis needs a defined system state rather than an assumption that all equipment either stops or operates as intended.<ref name="VR-6.6" />

Plume models likewise apply to specified geometries. The 2005 guidelines describe axisymmetric models for fires away from walls, where air can be entrained from all sides. A wall, corner or obstruction changes the available entrainment paths and can place the fire outside the free-plume model assumptions.<ref name="IFEG-2.5-2" />

Sensitivity to heat release rate, gas temperature and flow rate should be made visible. These quantities vary during fire growth and decay, so a single steady calculation cannot show when a detector, structural element or remote fuel package reaches a critical condition. Time selection is part of the engineering assumption.<ref name="VR-5.1" /><ref name="IFEG-2.5-2" />

Flow determination comes before surface heat transfer. Van Rossum emphasises that the gas movement must first be described, after which its thermal effect can be calculated. Assuming a heat-transfer coefficient before establishing whether the surface encounters plume, ceiling jet or slower room gas reverses that logic.<ref name="VR-5.3" />

Natural and forced components can also change differently with time. A growing fire can strengthen buoyant flow while a fan operates at a fixed setting or a smoke-control system changes state. The combined flow therefore cannot always be scaled from fire size alone.<ref name="VR-5.3" /><ref name="VR-6.6" />

Results should be checked against their physical meaning. A surface heat flux needs a receiving area to become total heat flow, while transported power needs a defined flow crossing. Comparing these outcomes without conversion would mix local exposure with energy passing through the building.<ref name="VR-5.3" />

== Boundary layers and turbulence ==

Fluid immediately at a solid surface is approximately stationary, while velocity increases away from the surface. The resulting boundary layer contains strong velocity and temperature gradients. Heat crossing from the main gas flow to the surface must pass through this region.<ref name="VR-5.3" />

In laminar flow, fluid moves in comparatively orderly layers with limited crosswise mixing. In turbulent flow, eddies transport fluid and energy across the main flow direction. Van Rossum explains that this stronger mixing generally increases convective heat transfer to a surface.<ref name="VR-5.3" />

Turbulence is common near fires, openings and obstacles. Velocity, geometry and fluid properties all affect whether flow remains laminar or becomes turbulent. A coefficient obtained for one configuration cannot be transferred to another merely because both involve hot air.<ref name="VR-5.3" /><ref name="Atreya-1-45" />

The convective [[Heat flux]] to a surface depends on the gas-to-surface temperature difference and the heat-transfer coefficient. Higher gas temperature can increase this driving difference, while greater turbulence can increase the coefficient. Both effects must be considered when comparing exposures.<ref name="VR-5.3" />

At the surface itself, molecular conduction remains part of the process even when the wider flow is turbulent. Convection therefore does not eliminate conduction; it changes the temperature and flow conditions under which that local transfer occurs.<ref name="Atreya-1-44" /><ref name="Atreya-1-45" />

== Convection in smoke spread ==

Convection carries heated combustion products into upper parts of enclosures and through available openings. The resulting [[Smoke movement]] can expose locations remote from the fire. This remote exposure includes heat as well as reduced visibility and combustion-product concentration.<ref name="VR-5.3" /><ref name="IFEG-2.5-2" />

For a smoke flow, the transported power above an ambient reference follows from mass flow, specific heat and temperature rise. Multiplying density by volume flow first gives mass flow. The resulting power is carried through the exhaust or opening; it is not the heat delivered to any particular wall.<ref name="VR-5.3" />

<math display="block">\dot Q_{\mathrm{flow}}=\rho c_p\dot V(T_x-T_0),\qquad \rho\approx\frac{353}{T_x}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot Q_{\mathrm{flow}}</math> || Thermal power transported above the ambient reference || W
|-
| <math>\rho</math> || Gas density at smoke temperature || kg/m³
|-
| <math>c_p</math> || Specific heat at constant pressure || J/(kg·K)
|-
| <math>\dot V</math> || Volume flow at smoke temperature || m³/s
|-
| <math>T_x,T_0</math> || Smoke and reference ambient temperatures || K for density; K or °C for their difference
|}

Van Rossum's worked example uses an exhaust flow of 100 m³/s at 463 °C, with ambient air at 20 °C. The source assumes air properties and a constant specific heat of 1005 J/(kg·K). Converting smoke temperature to 736.15 K gives a density of approximately 0.480 kg/m³. The density and volume flow must describe the same hot-gas state.<ref name="VR-5.3" />

Retaining the unrounded density gives approximately 21.3 MW to three significant figures. This reproduces the source's approximately 21.35 MW with fewer reported digits. Rounding the density before multiplication slightly changes the result. The example illustrates sensible heat transport under fixed conditions, rather than an exhaust capacity suitable for every building.<ref name="VR-5.3" />

<math display="block">\dot Q_{\mathrm{flow}}=\frac{353}{736.15}\times1005\times100\times(463-20)\approx2.13\times10^7\ \mathrm{W}=21.3\ \mathrm{MW}</math>

Wind and mechanical systems can modify or reverse expected paths. Natural pressure differences from heating occur together with expansion, stack effect and equipment-induced pressures. The whole pressure field must therefore be represented when assessing flow through openings.<ref name="VR-6.6" />

== Engineering use and limitations ==

Convection calculations support estimates of upper-layer energy, smoke production, boundary heating and device exposure. The required input can include heat release rate, plume entrainment, gas temperature and surface conditions. These inputs are often time-dependent and uncertain.<ref name="IFEG-2.5-2" /><ref name="VR-5.1">Van Rossum (2027), §5.1.</ref>

A steady surface calculation can provide an order-of-magnitude estimate, but a real fire changes both source and receiver temperatures. Assuming a fixed heat-transfer coefficient can hide these changes. A more detailed transient model is needed when the timing of exposure is central to the result.<ref name="VR-5.1" /><ref name="VR-5.3" />

Convective heat transfer is also not simply a direct result of air temperature. Two gas streams at the same temperature can deliver different heat fluxes because their velocities, turbulence and surface geometries differ. Conversely, a high coefficient cannot create heat transfer without a temperature difference.<ref name="VR-5.3" />

Convection and smoke toxicity are separate aspects of the same transport. Dilution by entrained air can reduce concentration while increasing total mass flow. A diluted stream can still carry substantial energy and combustion products to another location.<ref name="VR-5.3" /><ref name="IFEG-2.5-2" />

The direction of heat exchange can reverse as surface and gas temperatures change. A construction that initially absorbs heat from smoke can later lose heat to cooler gas. Retaining the sign and time history of the temperature difference prevents this reversal from being lost in a single positive design number.<ref name="VR-5.3" /><ref name="Rockett-Milke-1-29">Rockett and Milke (2002), p. 1-29.</ref>

== See also ==

* [[Adiabatic surface temperature]]
* [[Biot number]]

== Notes ==

<references />

== References ==

* Alpert, R. L. (2002). Ceiling jet flows. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-18–2-31). National Fire Protection Association.
* Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Kandola, B. S. (2002). Introduction to mechanics of fluids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-1–1-26). National Fire Protection Association.
* Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
* Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-73–1-89). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Physics & Heat Transfer]]

Flame

2026-11-02T17:33:55Z

Peter: Improve FSE wiki article: Flame; source, clarity and calculation review (GPT-6)

A '''Flame''' is a gas-phase [[Combustion]] region in which fuel reacts with an oxidiser, usually oxygen from the surrounding air. The reaction region releases heat and may emit light from hot particles and excited chemical species. Flaming is therefore a gas-phase form of combustion, distinct from flameless surface processes such as smouldering.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

Flames vary in shape, luminosity, temperature and stability. Fuel and oxidiser can be mixed before ignition or can come together within the flame. Flow can be smooth or turbulent, and the flame can exchange heat with fuel, nearby surfaces and the surrounding gas. These differences determine how a flame looks and how it affects its surroundings.<ref name="VR-4.3" /><ref name="Simmons-1-152">Simmons (2002), p. 1-152.</ref>

A visible flame is not a complete measure of a fire. Some flames produce little light, while a hot or decomposing fuel can remain hazardous without visible flaming. Flame observation therefore needs to be combined with knowledge of fuel supply, oxygen, heat transfer and combustion products.<ref name="VR-4.3" /><ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

== Premixed and diffusion flames ==

In a [[Premixed flame]], fuel and oxidiser are mixed before ignition. A Bunsen burner provides a familiar example. Simmons describes a luminous inner cone, where rapid oxidation produces a steep temperature rise, surrounded by hot combustion gases. With a fuel-rich initial mixture, the outer region can behave as a diffusion flame while remaining fuel burns with oxygen from the surrounding atmosphere.<ref name="Simmons-1-144">Simmons (2002), p. 1-144.</ref>
[[File:fse-flame-v1.svg|thumb|upright=1.5|alt=Premixed gases entering a Bunsen flame and separated fuel and air entering a diffusion flame.|Mixing arrangements in premixed and diffusion flames. Based on Van Rossum (2027), §4.3 and Simmons (2002), p. 1-144.]]

In a [[Diffusion flame]], fuel and oxidiser are initially separated and mix within the flame. A candle and many fires involving solids or liquids follow this broad pattern. Their fuel vapour originates at a surface, while oxygen arrives from the surrounding air. The reaction zone develops where mixing and temperature support combustion.<ref name="VR-4.3" /><ref name="Simmons-1-151">Simmons (2002), pp. 1-151–1-152.</ref>

The distinction concerns mixing arrangement rather than two wholly different chemistries. Simmons notes that the basic chemistry in a hydrocarbon-air diffusion flame is related to that in a premixed flame, but local conditions vary across the reaction region. Fuel-rich and oxygen-rich zones support different reactions and products. A single overall fuel-to-air ratio cannot describe every location in the flame.<ref name="Simmons-1-151" />

A premixed flame has a burning velocity, defined as its speed normal to the flame surface through the adjacent unburnt mixture. In an ideal flat flame, stability requires this velocity to balance the incoming mixture velocity. Excess flow can blow the flame off, while insufficient flow can allow flashback towards the burner. A conical burner flame can adjust its area and remain stable over a wider flow range.<ref name="Simmons-1-144" />

Diffusion flames can also depend on local premixed regions. Near the base of a gas-jet flame, low gas velocity allows fuel and air to mix before burning. The balance between local flow and burning velocity helps determine whether the flame remains attached or blows off. Recirculation behind an obstruction can similarly create a stable combustion region.<ref name="Simmons-1-151" />

== Laminar flow, turbulence and buoyancy ==

A laminar flame has an orderly flow structure. In a laminar diffusion flame, molecular diffusion is an important means of oxygen transport. Van Rossum uses a candle flame to illustrate this slow mixing process and the relatively hot outer reaction region. The description applies to the selected flame conditions and not to every candle-like fire at every scale.<ref name="VR-4.3" />

Turbulence introduces continually changing velocity components. These fluctuations deform the reaction region and increase mixing between fuel, oxidiser and hot products. In a premixed flame, a sharply defined laminar front can become a thicker, brush-like reaction region as turbulence increases. The flame is then not a smooth surface with uniform properties.<ref name="Simmons-1-146">Simmons (2002), p. 1-146.</ref>

Many real fires are turbulent diffusion flames whose flow is driven largely by buoyancy. Hot combustion products have lower density than the surrounding cooler gas and rise, drawing air into the fire region. Simmons explains that this turbulent motion can control mixing and hence the overall reaction rate, even when the underlying chemistry could proceed faster.<ref name="Simmons-1-151" /><ref name="Simmons-1-152" />

This interaction produces a changing flame shape rather than a fixed outline. Turbulent motion can fold and stretch the reaction zone, while air supply and fuel vapour production vary with time. The instantaneous visible boundary does not identify all locations where reactions or heat release occur.<ref name="Simmons-1-152" />

== Colour, soot and radiation ==

The yellow or orange luminosity of many diffusion flames is associated with hot [[Soot]] particles. These particles emit visible radiation because of their temperature. Fuels that produce little soot can have flames that are difficult to see, so low luminosity does not necessarily mean low temperature or low heat release.<ref name="VR-4.3" />
[[File:fse-flame-v2.svg|thumb|upright=1.5|alt=Diffusion flame with a fuel-rich core, a carbon-particle zone and the main reaction zone on the air side.|Local chemistry and soot affect flame appearance. Based on Simmons (2002), pp. 1-151–1-152.]]

Local chemistry influences this appearance. On the fuel-rich side of a hydrocarbon-air diffusion flame, limited oxygen favours thermal decomposition and carbon formation. Simmons connects this region with the characteristic yellow carbon zone. The hot blue region on the air side has different composition and reaction conditions.<ref name="Simmons-1-151" />

Premixed flames also emit radiation from excited chemical species. Simmons describes radiation from electronically excited hydroxyl radicals contributing to the luminous inner cone of a Bunsen flame. Flame light consequently has more than one physical origin, and colour alone cannot identify temperature or completeness of combustion.<ref name="Simmons-1-150">Simmons (2002), p. 1-150.</ref>

[[Flame radiation]] transfers energy to surrounding surfaces without requiring a gas to carry heat between them. Together with convective heat transfer, it can heat unburnt fuel and other objects. Van Rossum gives a rough division of approximately 30% radiation and 70% convection for fire energy, while explicitly noting that the actual proportions differ between fires.<ref name="VR-4.3" />

Radiative feedback is particularly relevant to sustained burning of liquids and solids. Heat returned to the fuel supports evaporation or pyrolysis, which supplies more vapour to the flame. The flame and fuel therefore form a coupled system. Changing surface orientation or heat loss can alter growth even when the fuel chemistry remains unchanged.<ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

== Temperature and heat release ==

Flame temperature is not uniform. In a premixed Bunsen flame, Simmons places the maximum temperature slightly downstream of the inner cone, while heat losses produce steep gradients towards the surroundings. Diffusion flames likewise have fuel-rich, reaction and air-side regions with different temperatures and compositions.<ref name="Simmons-1-144" /><ref name="Simmons-1-151" />

The adiabatic flame temperature is a theoretical value calculated without heat exchange with the surroundings. It is reached only in restricted regions of sufficiently large flames under suitable assumptions. Small premixed flames and turbulent flames commonly fail to reach it because their heat losses are appreciable.<ref name="Simmons-1-145">Simmons (2002), p. 1-145.</ref>

High-temperature chemistry adds another limitation. Above approximately 1800 K, calculations may need to account for energy absorbed by dissociation of combustion products. Drysdale similarly explains that radiation and dissociation make real temperatures lower than a simple theoretical maximum. A temperature calculation therefore depends on both energy conservation and chemical composition.<ref name="Simmons-1-145" /><ref name="Drysdale-1-96">Drysdale (2002), p. 1-96.</ref>

Heat release rate and flame size are related but not interchangeable. Heat release rate is the energy produced per unit time, while flame geometry describes where the reaction region extends. Van Rossum notes that greater fire power is associated with greater [[Flame height]], but fuel, mixing and flow still influence the observed shape.<ref name="VR-4.5">Van Rossum (2027), §4.5.</ref><ref name="VR-4.3" />

A flame can also receive fuel produced in one place and burn it elsewhere. In an oxygen-limited enclosure, unburnt volatiles can leave through an opening and ignite after mixing with fresh air. The visible external flame then belongs to the same overall fire system, although part of its heat release occurs outside the original compartment.<ref name="Drysdale-1-95" />

== Flames and fire growth ==

A flame can sustain or enlarge a fire by heating new fuel. Upward spread over a vertical surface benefits from heat transfer to material above the burning region. This preheating can increase pyrolysis and accelerate spread. The process depends on orientation and heat feedback, not only on whether the material can burn in a small test.<ref name="VR-4.3" />

Enclosures modify this feedback. Hot gases and surfaces can radiate to other combustible objects, while limited ventilation changes oxygen supply and the movement of unburnt vapour. Flames can consequently influence remote ignition as well as the fuel immediately beneath them.<ref name="VR-4.3" /><ref name="Drysdale-1-95" />

Flame stability results from a balance of reaction, mixing and heat loss. At a flammability limit, heat losses can exceed heat production and prevent sustained propagation. Chemical inhibitors provide another route by promoting termination of chain reactions, reducing reaction until the flame cannot continue.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref><ref name="Simmons-inhibition">Simmons (2002), pp. 1-150–1-151.</ref>

Extinction of visible flaming does not prove that all combustion has stopped. Smouldering can continue within a porous solid, and hot fuel can later produce a flammable vapour mixture. A flame assessment therefore needs to consider the remaining fuel condition and the possibility of renewed ignition.<ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref><ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

== Measuring flame behaviour ==

Burning velocity is measured by relating the flow of unburnt mixture to the area and position of the flame front. For propane-air mixtures, Simmons reports maximum laminar burning velocities mainly between 37 and 45 cm/s, with most values in the range 41 ± 2 cm/s. These values relate to room-temperature, atmospheric-pressure initial conditions and should not be transferred to turbulent fire plumes.<ref name="Simmons-1-146" />
[[File:fse-flame-v3.svg|thumb|upright=1.5|alt=Range 37 to 45 cm/s with main range 39 to 43 and central marker 41.|Reported maximum laminar burning velocities for propane-air mixtures. Based on Simmons (2002), p. 1-146.]]

The measurement method contributes to variation between reported values. Different definitions of the visible front can produce different areas, while the burner rim removes heat and changes the local reaction. Flow near the cone tip can also differ from the idealised flat-flame arrangement. A numerical burning velocity therefore needs its apparatus and flame definition.<ref name="Simmons-1-146" />

Burning velocity also differs from the speed at which a flame advances along a duct. Simmons describes an initial, approximately uniform propagation stage away from an opening. In this idealisation, a larger flame-front area consumes more mixture, so the front advances faster along the duct. Its propagation speed is the burning velocity multiplied by the ratio of flame area to duct cross-sectional area:<ref name="Simmons-1-147">Simmons (2002), p. 1-147, Equation 3.</ref>

<math display="block">V=S_u\frac{A_f}{A_d}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>V</math> || Flame propagation speed along the duct || m/s
|-
| <math>S_u</math> || Burning velocity normal to the flame in the unburnt mixture || m/s
|-
| <math>A_f</math> || Area of the flame front || m²
|-
| <math>A_d</math> || Cross-sectional area of the duct || m²
|}

For a worked illustration, take the source's representative maximum propane-air burning velocity of 0.41 m/s. Choose an area ratio of 2, within the stated typical range of 2 to 3 for this configuration. The calculated propagation speed is 0.82 m/s. This example combines source values to explain the relation; it is not a prediction for a particular duct fire:<ref name="Simmons-1-146" /><ref name="Simmons-1-147" />

<math display="block">V=0.41\times2=0.82\ \mathrm{m/s}</math>

The relation does not cover every later stage of propagation. If hot products cannot vent sufficiently, pressure can drive gases forwards and increase turbulence ahead of the flame. Burning velocity and flame area can then change during acceleration. The initial uniform-speed estimate must therefore remain tied to its flow and venting assumptions.<ref name="Simmons-1-147" />

Temperature mapping addresses a different property. Simmons' example of a premixed natural-gas flame shows a changing temperature field above and around the inner cone rather than one flame temperature. The highest region is downstream of the primary reaction zone, and the outer gases cool towards the surroundings. A single point measurement cannot represent that whole field.<ref name="Simmons-1-144" /><ref name="Simmons-1-145" />

Heat release rate requires another measurement again. Oxygen-consumption calorimetry estimates it from oxygen consumed during combustion, using approximately 13.1 kJ/g of oxygen for many fuels with a correction associated with carbon monoxide. The method can be applied from small specimens to larger furniture tests. It does not determine heat release from flame luminosity alone.<ref name="Drysdale-1-96" />

Radiative and convective heat transfer connect these measurements with fire effects. A flame can have substantial heat release while transferring different proportions of energy to a fuel surface, depending on configuration. Measurement of total energy production therefore does not remove the need to assess exposure at the receiving object.<ref name="VR-4.3" />

Chemical models add further choices. In a turbulent methane-air example discussed by Simmons, assuming thermodynamic equilibrium predicted a peak carbon-monoxide mole fraction about 2.5 times the experimental value. A laminar-flamelet approach produced agreement within 10% for that case. This comparison is specific to the reported model and experiment, not a general error allowance.<ref name="Simmons-1-152" />

The difference arises because actual composition need not reach equilibrium throughout a turbulent diffusion flame. Flow can move gases away before slower reaction and burnout processes finish. Flame models consequently combine chemical assumptions with conservation of mass, energy and species, and their predictions require experimental support.<ref name="Simmons-1-152" />

== Interpretation and limits ==

Flame appearance provides qualitative evidence but not a complete engineering measurement. Luminosity depends on soot and excited species, while temperature and reaction rates vary through the flame. Two flames with different colours or shapes cannot be ranked reliably without information about fuel, scale and flow.<ref name="VR-4.3" /><ref name="Simmons-1-150" />

Models of turbulent flames must make assumptions about chemistry and equilibrium. Simmons notes that local equilibrium can apply only in limited regions and that real fires add feedback between chemistry, heat transfer and fluid motion. A simple flame picture cannot capture all these interactions.<ref name="Simmons-1-152" />

For fire safety work, the useful description includes the fuel source, mixing mode, geometry, heat feedback and surroundings. These features connect the flame to fire growth, detection and extinguishment without treating its visible outline as the fire itself.<ref name="VR-4.3" /><ref name="Beyler-Hirschler-1-110" />

A flame should also be distinguished from the burning object. The object supplies fuel, while the flame occupies a gas-phase reaction region that can change position and shape. This distinction remains valid when flames extend beyond the original fuel package.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref><ref name="Drysdale-1-95" />

== See also ==

* [[Adiabatic flame temperature]]
* [[Turbulence]]

== Notes ==

<references />

== References ==

* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-144–1-154). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Combustion

2026-11-02T17:33:46Z

Peter: Improve FSE wiki article: Combustion; source, clarity and calculation review (GPT-6)

'''Combustion''' is a set of chemical reactions in which a fuel reacts with an oxidiser, usually oxygen, and releases energy. In a fire, these reactions are predominantly exothermic, meaning that they release heat. They can also produce light as a visible flame or as a glow. Combustion can involve gaseous, liquid or solid fuels, but liquids and solids usually have to produce gaseous fuel before flaming combustion can occur.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref>

The process is more than a single reaction between a fuel and oxygen. It includes heating, decomposition, mixing, chemical reaction and heat transfer. These processes form a feedback system: heat released by the reactions can produce more gaseous fuel, which can then react and release further heat. The balance between heat production, fuel supply, oxygen supply and heat loss determines whether combustion starts, continues, spreads or stops.<ref name="VR-4.1" /><ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

For fire safety, combustion matters because it converts stored chemical energy into heat and combustion products. The amount of energy per unit of fuel, the speed of conversion and the conditions around the fuel all influence the resulting fire. Combustion therefore connects material properties with flame behaviour, heat release, smoke production and the effectiveness of extinguishing measures.<ref name="Drysdale-1-90">Drysdale (2002), p. 1-90.</ref><ref name="VR-4.4">Van Rossum (2027), §4.4.</ref>

== Fuel, oxidiser and the combustion system ==

The conventional description of combustion starts with fuel, oxygen and sufficient heat. These three elements form the [[Fire triangle]]. Fuel supplies the material that can be oxidised, oxygen acts as the oxidiser, and heat raises the fuel and reaction zone to conditions at which the reactions can proceed. A combustible material and oxygen can coexist without a fire when insufficient energy is available for ignition.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref>

The [[Fire tetrahedron]] adds the uninhibited chemical chain reaction to these three elements. This addition recognises that combustion is not extinguished only by removing fuel, oxygen or heat. Some extinguishing agents interfere with active chemical species in the flame and thereby interrupt the chain reaction. The tetrahedron is therefore a model of four conditions that can be interrupted, rather than a picture of four physical substances.<ref name="Grant-4-152">Grant (2002), pp. 4-152–4-153.</ref>

Oxygen normally reaches a fire as part of ambient air. Van Rossum gives the approximate composition of air as 21% oxygen, 78% nitrogen and 1% other gases by volume. Nitrogen does not have to take part in the principal combustion reaction, but it forms part of the gas mixture that must be heated and moved. When the oxygen concentration falls, fire growth can be restricted and extinction can eventually follow, depending on the fuel and conditions.<ref name="VR-4.2" /><ref name="Drysdale-1-92">Drysdale (2002), p. 1-92.</ref>

The fuel side is not limited to materials commonly called fuels. Wood, paper, plastics, liquids and combustible gases can all supply chemical energy. Their composition and physical form affect how easily gaseous fuel is produced and mixed with oxygen. The surrounding geometry also matters because it influences heat retention, air movement and the transfer of heat to unburnt material.<ref name="VR-4.1" /><ref name="Beyler-Hirschler-1-111">Beyler and Hirschler (2002), p. 1-111.</ref>

== How liquids and solids become combustible gases ==

A gaseous fuel can mix directly with oxygen from the air. This makes gas combustion the most direct of the three physical fuel states. A liquid normally has to evaporate, or form a mist of droplets, before its fuel can participate in flaming combustion. During a pool fire, vapour produced at the liquid surface mixes with air and burns above that surface rather than throughout the liquid volume.<ref name="VR-4.1" />

Most solids require thermal decomposition before flaming combustion. [[Pyrolysis]] breaks large molecules into smaller ones as the material is heated, producing combustible gases and often leaving a solid residue. Pyrolysis itself does not require oxygen. The released gases burn only when they mix with oxygen in suitable proportions and receive enough energy for ignition. They can burn immediately, burn elsewhere or remain unburnt.<ref name="VR-3.1">Van Rossum (2027), §3.1.</ref>
[[File:fse-combustion-v1.svg|thumb|upright=1.5|alt=Cycle from heated solid to pyrolysis gases, flame and heat returning to the solid.|Heat feedback links pyrolysis and flaming in a sustained solid-fuel fire. Based on Van Rossum (2027), §3.1 and §4.3.]]

Polymer decomposition shows why the original material alone does not determine fire behaviour. The rate, mechanism and products of decomposition depend on both chemical composition and physical properties. Some materials melt or soften before decomposition, while thermosetting and cellulosic materials do not pass through the same fluid state. These differences affect how heat and volatile gases move through the material.<ref name="Beyler-Hirschler-1-112">Beyler and Hirschler (2002), pp. 1-112–1-113.</ref>

A sustained solid-fuel fire depends on an energy feedback loop. A [[Flame]] transfers heat back to the fuel, the heated fuel releases volatile gases, and those gases support further flaming. Some released heat is lost to the surroundings, so the feedback must be large enough to maintain decomposition. Surface orientation changes this balance. Upward spread over a vertical surface can preheat material above the burning region and accelerate fire development.<ref name="Beyler-Hirschler-1-110" /><ref name="VR-4.3">Van Rossum (2027), §4.3.</ref>

The production of a char layer adds another feedback mechanism. Char can insulate underlying material and change the route by which volatile gases escape. An intumescent char can slow further decomposition considerably. Carbonaceous char can itself oxidise at the surface at higher temperatures, so its presence does not simply mean that combustion has ended.<ref name="Beyler-Hirschler-1-111" />

== Flaming and non-flaming combustion ==

Flaming combustion takes place in the gas phase. A flame is a gas-phase reaction region where fuel reacts with oxygen and can emit visible light. Fuel and air may already be mixed before ignition, as in a premixed flame, or they may mix at the flame through diffusion and turbulence, as in a diffusion flame. These mixing arrangements influence flame shape, temperature distribution and the location of the reaction zone.<ref name="VR-4.1" /><ref name="VR-4.3" />

In a laminar diffusion flame, molecular diffusion controls much of the oxygen transport. A candle flame is a familiar example. In a turbulent diffusion flame, continually changing motion draws surrounding air into the reaction region. The flow and the flame therefore interact, and the combustion rate cannot be explained by chemical reaction rates alone.<ref name="VR-4.3" />

The colour of a flame does not provide a complete measure of its temperature or completeness of combustion. Hot soot particles emit much of the yellow or orange light seen in many diffusion flames. Fuels producing little soot can have flames that are difficult to see. Oxygen availability, fuel vapour and local temperature all vary within the flame, so different regions can have different appearances.<ref name="VR-4.3" />

[[Smouldering]] is a slow, lower-temperature, flameless form of combustion in which oxygen directly attacks the surface of a condensed-phase fuel. It should not be confused with forced pyrolysis, where an external heat source causes decomposition and smoke with little or no oxidation. Porous, finely divided and thermally insulating fuel beds can retain enough heat and admit enough oxygen to sustain smouldering.<ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>
[[File:fse-combustion-v2.svg|thumb|upright=1.5|alt=Left, flame above fuel vapour; right, oxygen reacting inside a porous char bed without flame.|Flaming combustion and smouldering occur in different regions and forms. Based on Van Rossum (2027), §4.1 and Ohlemiller (2002), p. 2-200.]]

Char-forming materials are particularly relevant to smouldering. Char has a carbon-rich, porous structure that can support surface oxidation. The heat from this oxidation helps the reaction zone move through the fuel. Smouldering can generate a relatively high conversion of fuel to toxic compounds and can later provide a route to flaming, even when the initial heat source was too weak to ignite a flame directly.<ref name="Ohlemiller-2-200" />

== Energy release and combustion products ==

The [[Heat of combustion]] is the heat released when a unit quantity of fuel is oxidised completely to stable end products. It is measured with a combustion bomb calorimeter, in which a known amount of fuel burns in pure oxygen and the temperature rise is used to determine the energy release. This is a controlled measurement of energy content, not a direct measurement of how a real room fire develops.<ref name="Drysdale-1-92" />
[[File:fse-combustion-v3.svg|thumb|upright=1.5|alt=Bars for propane 46.45, cellulose 16.09 and polyethylene 43.28 kJ/g.|Selected net heats of combustion at 25 °C, with product water as vapour. Based on Drysdale (2002), p. 1-93.]]

The distinction between gross and net heat of combustion concerns the state of water in the products. Net heat of combustion treats product water as vapour and is lower than the gross value by the energy needed to evaporate that water. Drysdale identifies the net value as the one to use in fire calculations. Data in the SFPE Handbook are given at an initial temperature of 25 °C and are suitable for most fire problems covered there.<ref name="Drysdale-1-93">Drysdale (2002), p. 1-93.</ref>

Values vary substantially between fuels. In the handbook table, propane has a heat of combustion of 46.45 kJ/g, cellulose 16.09 kJ/g and polyethylene 43.28 kJ/g. These figures describe complete oxidation under the stated measurement basis. They do not mean that equal masses of these materials will produce the same fire, because decomposition, burning rate, oxygen access and combustion efficiency also affect heat release.<ref name="Drysdale-1-93" /><ref name="VR-4.5">Van Rossum (2027), §4.5.</ref>

A balanced reaction for complete propane combustion produces carbon dioxide and water. It also shows how much oxygen and air the reaction requires. Drysdale calculates that 1 g of propane requires 3.64 g of oxygen, or 15.6 g of air when nitrogen is included. For an assumed empirical composition of wood, the corresponding stoichiometric air requirement is 5.38 g of air per gram of wood. Such values describe complete combustion under specified assumptions, not the variable air supply of every fire.<ref name="Drysdale-1-92" />

[[Incomplete combustion]] occurs when the available conditions do not convert all fuel to the stable products associated with complete oxidation. Fire conditions can produce carbon monoxide, soot and other compounds in addition to carbon dioxide and water. Wood provides a useful example of separate pathways: its volatile gases can undergo flaming combustion while the residual char oxidises much more slowly at the surface.<ref name="Drysdale-1-92" /><ref name="Ohlemiller-2-200" />

The total chemical energy in a fuel and the rate at which that energy is released answer different questions. Energy content is expressed in units such as megajoules, while heat release rate is power expressed in watts, kilowatts or megawatts. A large energy store can therefore coexist with a small current heat release rate. Fire duration and total thermal exposure depend on energy, whereas flame size and short-term fire severity are strongly related to power.<ref name="VR-4.4" /><ref name="VR-4.5" />

For a single fuel undergoing complete combustion, heat release rate follows from multiplying the mass burning rate by the net heat of combustion. This relation converts fuel consumed each second into energy released each second. The heat of combustion is written here as a positive energy release per unit mass:<ref name="Drysdale-burning-rate">Drysdale (2002), p. 1-95, Equation 24.</ref>

<math display="block">\dot{Q}=\dot{m}H_c</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot{Q}</math> || Heat release rate || kW
|-
| <math>\dot{m}</math> || Mass burning rate || kg/s
|-
| <math>H_c</math> || Net heat of combustion, expressed as a positive value || kJ/kg
|}

For an illustrative calculation, assume that propane burns completely at a steady rate of 0.001 kg/s. The assumed rate is an example input, not a measured result from the handbook. Using its tabulated 46.45 kJ/g, equivalent to 46,450 kJ/kg, gives a heat release rate of about 46.5 kW:<ref name="Drysdale-1-93" /><ref name="Drysdale-burning-rate" />

<math display="block">\dot{Q}=0.001\times46{,}450=46.45\ \mathrm{kW}\approx46.5\ \mathrm{kW}</math>

This calculation requires both fuel consumption and complete oxidation. It does not predict how quickly a material will release vapour or whether enough oxygen reaches it. In a real fire, incomplete oxidation can reduce the released energy per unit mass. A measured effective heat of combustion or an appropriate combustion-efficiency allowance is then needed.<ref name="Drysdale-burning-rate" />

== Ignition, persistence and extinction ==

Ignition is the transition into self-sustaining combustion, not simply the appearance of heat or smoke. The International Fire Engineering Guidelines distinguish three modes. Piloted ignition occurs when a flame, spark or hot object ignites pyrolysis gases. Non-piloted ignition occurs when the gas mixture reaches a temperature at which it ignites without such a local pilot. Self-induced ignition begins with oxidation inside a solid, which supplies energy for decomposition and further heating.<ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

Persistence requires the energy released by the reactions to exceed the energy lost from the reaction zone. Near a lower flammability limit, radiation and other heat losses can exceed heat production, preventing the flame from sustaining itself. This heat balance explains why a fuel and oxidiser can react in one configuration but fail to maintain combustion in another. Chemical composition alone does not settle the outcome.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref>

A change from smouldering to flaming requires two conditions at the same place and time: a mixture of gases and air within its flammability range, and sufficient heat to ignite it. Increased oxygen supply, a larger fuel bed and reduced heat losses can all raise local temperature and pyrolysis-gas production. The transition is therefore not an automatic stage that follows every period of smouldering.<ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

Extinction also depends on the combustion configuration. Removing oxygen from a deep porous fuel may suppress the reaction temporarily, but readmitting oxygen can cause reignition while the fuel remains hot. Ohlemiller notes that oxygen removal may have to continue until the fuel has cooled. Cooling such a fuel bed can be difficult because the same insulating structure that supports smouldering restricts heat removal.<ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref>

In an enclosure, incomplete combustion within the room does not necessarily end the combustion process. Fuel volatiles can leave through an opening, mix with fresh air and burn outside. This behaviour affects both the location of heat release and the interpretation of measurements taken inside the enclosure. It also illustrates why a description limited to the original fuel package can miss part of the fire.<ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

== Measuring combustion behaviour ==

Different measurements describe different parts of combustion. Bomb calorimetry establishes chemical energy under controlled, complete-oxidation conditions. Oxygen-consumption calorimetry instead estimates heat release during a fire test from the oxygen consumed. The first method is associated with energy content, while the second can follow changing heat release rate as a specimen burns.<ref name="Drysdale-1-92" /><ref name="Drysdale-1-95" />

Oxygen-consumption calorimetry uses the approximately consistent heat released per unit mass of oxygen consumed across many fuels. Drysdale gives a conversion factor of 13.1 kJ/g of oxygen, with a correction for incomplete combustion based on carbon monoxide yield. The technique can be used for a small specimen in a cone calorimeter and at larger scales for furniture and wall linings.<ref name="Drysdale-1-95" /><ref name="Drysdale-1-96">Drysdale (2002), pp. 1-95–1-96.</ref>

The cone calorimeter exposes a small sample to an imposed radiant heat flux. This controlled exposure makes it possible to compare material responses, but the result remains tied to the test conditions. Specimen shape, applied heat flux and the actual burning environment influence the measurements. A test heat-release curve is therefore not automatically the heat-release curve of every object made from that material.<ref name="Drysdale-1-96" /><ref name="Beyler-Hirschler-1-112" />

Combustion efficiency expresses the difference between theoretical complete oxidation and actual energy release. Even with unrestricted ventilation, natural fires produce partially oxidised species such as carbon monoxide, aldehydes, ketones and particulate matter. Drysdale reports likely efficiencies from approximately 0.3 to 0.4 for heavily fire-retarded materials to 0.9 or higher for some oxygen-containing products. These ranges are material-dependent and do not remove the need to consider changing fire conditions.<ref name="Drysdale-1-95" />

Temperature estimates also require care. An adiabatic flame temperature is a theoretical maximum calculated with no heat transfer to the surroundings. Real flames lose energy by radiation, and high temperatures cause dissociation, in which combustion products split into other species through heat-absorbing processes. Drysdale's simplified propane example therefore predicts a higher temperature than the real flame can reach. The example demonstrates why energy conservation must be combined with heat transfer and chemical behaviour.<ref name="Drysdale-1-96" />

== Combustion in fire safety engineering ==

Combustion knowledge supports the description of a design fire, the selection of material data and the assessment of fire spread. An engineering analysis distinguishes the energy potentially available from all fuel from the energy actually released during a selected period. Van Rossum notes that real fires commonly release much less than the total theoretical energy because combustion efficiency is not complete.<ref name="VR-4.4" />

For a solid or liquid fuel, an assessment has to account for the processes that supply gaseous fuel. For a smouldering hazard, it also has to account for oxygen transport through a porous fuel and heat retention around the reaction zone. For a gas flame, mixing and chemical reaction require particular attention. These different controlling processes prevent one universal burning rate or combustion efficiency from being applied to every scenario.<ref name="Ohlemiller-2-201">Ohlemiller (2002), pp. 2-201–2-202.</ref><ref name="Beyler-Hirschler-1-111" />

Extinguishing strategies follow from the same system view. Fuel removal, oxygen limitation and cooling act on the three sides of the fire triangle. Chemical inhibition acts on the chain reaction represented by the fire tetrahedron. The appropriate mechanism depends on the fuel and the form of combustion; for example, a deep-seated smouldering region can behave differently from an open gas-phase flame.<ref name="Grant-4-152" /><ref name="Ohlemiller-2-200" />

Enclosure conditions add further feedback. Heat that cannot escape readily warms the compartment and its gases, and radiation from this hotter environment can heat other combustible objects. Ventilation can simultaneously affect oxygen supply, heat loss and the movement of unburnt gases. A description of combustion therefore has to include the surroundings as well as the fuel itself.<ref name="VR-4.3" /><ref name="VR-3.1" />

A schematic design fire converts this understanding into a simplified description for analysis. The 2005 International Fire Engineering Guidelines distinguish smouldering, non-flashover flaming and flashover fire types. For a flaming design fire, they describe a growth phase, a fully developed phase and a decay phase. This is a deliberate simplification for engineering evaluation, not a claim that every real fire follows the same curve.<ref name="IFEG-1.2-29">Australian Building Codes Board et al. (2005), pp. 1.2-29–1.2-30.</ref>

The combustion mode changes which uncertainties matter. A smouldering design fire may remain flameless or undergo a transition to flaming, and the timing of that transition is difficult to predict. The 2005 guidelines use a notional maximum heat release rate below 5 kW for their illustrated smouldering design fire. That figure belongs to this older modelling guidance and is not a general upper limit for every smouldering configuration.<ref name="IFEG-1.2-29" /><ref name="Ohlemiller-2-209">Ohlemiller (2002), p. 2-209.</ref>

A fire-load assessment starts from the quantity of combustible material and its calorific value. It can include contents as well as combustible construction, provided these contributions are identified clearly. Multiplying an inventory by an energy value estimates the chemical energy present, but does not establish that all material will burn. The analysis still needs a combustion scenario and a defensible burning period.<ref name="VR-4.4" /><ref name="IFEG-2.4-2">Australian Building Codes Board et al. (2005), pp. 2.4-2–2.4-3.</ref>

== Limits of simple descriptions ==

The fire triangle and fire tetrahedron are useful conceptual models, but neither predicts the speed or size of a fire. They do not describe fuel geometry, heat transfer, ignition delay, mixing or changing ventilation. Two arrangements with the same fuel, oxygen and initial heat source can develop differently when their heat losses and exposed surfaces differ.<ref name="VR-4.2" /><ref name="Beyler-Hirschler-1-112" />

Visible flame is not a reliable indicator of all combustion. Smouldering can persist without flame and may remain difficult to detect within a fuel layer. Some flames are hard to see when little soot is present. Assessment based only on appearance can consequently miss both hidden combustion and the energy and products associated with weakly luminous flames.<ref name="Ohlemiller-2-202">Ohlemiller (2002), p. 2-202.</ref><ref name="VR-4.3" />

== See also ==

* [[Carbon dioxide]]
* [[Fire classes]]
* [[Stoichiometry]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Grant, C. C. (2002). Halon design calculations. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-149–4-172). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Flame spread

2026-11-02T17:31:59Z

Peter: Improve FSE wiki article: Flame spread; source, clarity and calculation review (GPT-6)

'''Flame spread''' is the movement of a flame across or adjacent to a condensed fuel whose evaporation or pyrolysis supplies the flame with gaseous fuel. It involves two advancing regions: the visible gas-phase flame and the evaporation or decomposition front in the solid or liquid. The rate of the condensed-phase front defines surface flame-spread velocity.<ref name="Quintiere-2-246">Quintiere (2002), p. 2-246.</ref>

The process differs from flame propagation through a premixed gas. In surface flame spread, fuel and oxygen are not already distributed uniformly throughout the gas. Heat from the advancing flame must first produce new vapour ahead of the reaction region.<ref name="Quintiere-2-246" />

Flame spread influences how rapidly a small ignition develops into a larger fire. It can accelerate as more fuel and stronger heat feedback become involved, or stop when forward heating, fuel continuity or combustion conditions become inadequate.<ref name="Quintiere-2-246" /><ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref>

== Flame and decomposition fronts ==

The visible flame occupies the gas phase, while the condensed fuel remains beneath or beside it. Heat transferred from the flame evaporates liquid or decomposes solid ahead of the current burning area. The new vapour mixes with air and allows the flame to advance.<ref name="Quintiere-2-246" />
[[File:fse-flame-spread-v1.svg|thumb|upright=1.5|alt=Gas-phase flame above a solid with a separate advancing pyrolysis front.|Surface flame spread involves two advancing fronts. Based on Quintiere (2002), p. 2-246.]]

The evaporation or pyrolysis front is harder to observe than the flame, but it marks the region being converted into gaseous fuel. Its position and movement connect the visible flame with fuel consumption. A flame can appear substantial while the underlying front moves comparatively slowly.<ref name="Quintiere-2-246" />

This mechanism can be viewed as successive [[Ignition]] of new material. Each newly heated region must reach a condition supporting piloted reaction and continued vapour supply. Flame spread therefore depends on the target's initial temperature and ignition response as well as on the existing flame.<ref name="Kanury-2-229">Kanury (2002), p. 2-229.</ref>

A premixed gas flame follows a different mechanism. Fuel and oxidiser are already present in the gas, so propagation can be much faster and does not require an advancing solid-decomposition front. The two processes should not share an unqualified spread-rate value.<ref name="Quintiere-2-246" />

== Heat transfer ahead of the flame ==

Forward heat transfer raises fuel from its initial temperature towards its ignition condition. Conduction through gas and solid, convection from hot gases and radiation from the flame can all contribute. Their relative importance depends on flow, orientation, scale and material properties.<ref name="Quintiere-2-247">Quintiere (2002), p. 2-247.</ref>

Quintiere's conceptual energy balance compares heat delivered ahead of the front with the energy needed to prepare new fuel. Lower initial temperature requires more heating, while preheating by the wider fire reduces the additional energy needed. Spread can therefore accelerate as the surroundings become hotter.<ref name="Quintiere-2-247" />

Heat losses can prevent the front from sustaining itself. Energy entering a thick solid can drain into its interior, and convection can cool the reaction region. Stronger opposed flow may enhance some heat-transfer paths while reducing the time available for chemical reaction, so its effect is not universally positive or negative.<ref name="Quintiere-2-248">Quintiere (2002), pp. 2-248–2-250.</ref>

Flame temperature and heat flux are also coupled with oxygen and chemistry. Reduced oxygen can lower reaction and heat release, while excessive flow can quench the reaction region. Material data alone cannot predict spread without these fire conditions.<ref name="Quintiere-2-248" />

== Direction and airflow ==

[[Upward flame spread]] benefits from buoyant hot gases and flame contact preheating fuel above the front. This can produce a large heated region and rapid acceleration on vertical surfaces. Van Rossum identifies this mechanism as an important reason for faster upward spread.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Quintiere-2-247" />
[[File:fse-flame-spread-v2.svg|thumb|upright=1.5|alt=Upward flame preheating fuel above and a front advancing against airflow.|Flow direction changes flame-spread heat transfer. Based on Van Rossum (2027), §4.3 and Quintiere (2002), p. 2-247.]]

[[Opposed-flow flame spread]] occurs when the front advances against the surrounding gas flow. Forward heat must reach fuel despite that opposing transport. Quintiere distinguishes this from wind-aided spread, where the surrounding flow supports movement in the same direction.<ref name="Quintiere-2-247" />

Lateral and downward configurations have different heat-transfer paths and generally different rates from upward spread. The direction of gravity changes buoyancy, flame shape and which fuel is preheated. Material orientation must therefore accompany any reported rate.<ref name="Quintiere-2-247" />

External wind and fire-induced natural convection can both create the relevant flow. A value measured in still air cannot be transferred automatically to a ventilated shaft, open facade or compartment with strong fire-driven circulation.<ref name="Quintiere-2-247" /><ref name="IFEG-2.6-12">Australian Building Codes Board et al. (2005), p. 2.6-12.</ref>

The distance heated ahead of the front helps explain the difference between the flow arrangements. Quintiere gives illustrative heating lengths of about 1–3 mm for opposed spread and 0.1–10 m for wind-aided spread. The latter can extend over much of the adjacent flame and hot-gas region. These lengths belong to the simplified configurations and do not replace a heat-flux calculation.<ref name="Quintiere-2-251">Quintiere (2002), p. 2-251.</ref>

== Material thickness and thermal response ==

Thermally thin materials have relatively little temperature variation through their thickness in the simplified model. Paper, garments and draperies can sometimes approach this behaviour. Thermally thick materials retain important internal gradients, and heat conducted into them is unavailable at the surface.<ref name="Quintiere-2-248" />

Geometric thickness alone does not define the thermal class. Conductivity, density, specific heat, exposure time and backing conditions all influence the response. Quintiere gives approximate material-specific examples, but these should not be converted into universal thickness thresholds.<ref name="Quintiere-2-249">Quintiere (2002), p. 2-249.</ref>

Low density can favour rapid response because less energy is required to prepare a given volume for ignition. Substrates can add further heat storage or loss. A thin combustible finish on a massive backing can consequently behave differently from the same finish without that backing.<ref name="Quintiere-2-247" /><ref name="Quintiere-2-249" />

Moisture, melting and char formation change the response during heating. They alter heat consumption, surface integrity and volatile release. Treating the material as homogeneous and unchanged is a modelling simplification whose limits must be stated.<ref name="Kanury-2-232">Kanury (2002), p. 2-232.</ref><ref name="Beyler-Hirschler-1-112">Beyler and Hirschler (2002), pp. 1-112–1-113.</ref>

== Spread rate and fire growth ==

Quintiere illustrates growth with an upholstered-chair ignition region 6 cm in diameter and an unenhanced spread rate of about 1 mm/s. After one minute in the example, the pyrolysing region reaches 18 cm in diameter as the front advances 6 cm. The larger fuel area can then strengthen heat feedback.<ref name="Quintiere-2-246" />

For an ideal circular region, increasing the diameter from 6 cm to 18 cm multiplies the area by nine. The initial area is about 0.0028 m² and the later area about 0.025 m². This calculation assumes that the entire enclosed region remains involved. It illustrates how even a constant front speed can produce increasing burning area.<ref name="Quintiere-2-246" />

The example demonstrates area growth rather than a universal chair-fire rate. Spread rate can change as heat release increases, and fuel burnout can limit later development. Early spread and long-term fire growth therefore require a time-dependent description.<ref name="Quintiere-2-246" />

The handbook's order-of-magnitude table lists smouldering at 0.001 to 0.01 cm/s, lateral or downward spread on thick solids around 0.1 cm/s, and upward spread on thick solids from 1 to 100 cm/s. Premixed laminar deflagration is listed from 10 to 100 cm/s. These ranges show different mechanisms and scales, not values for direct substitution into another scenario.<ref name="Quintiere-2-247" />
[[File:fse-flame-spread-v3.svg|thumb|upright=1.5|alt=Log-scale ranges for smouldering, lateral spread, upward spread and premixed flame.|Order-of-magnitude flame-spread rates from the SFPE Handbook. Based on Quintiere (2002), p. 2-247.]]

[[Fire spread]] beyond the first object adds further pathways, including radiation across gaps, direct flame contact and burning debris. Surface flame spread is one mechanism within this wider process. A room or building fire should not be modelled as one continuous sheet of fuel unless that geometry actually applies.<ref name="IFEG-1.6-7">Australian Building Codes Board et al. (2005), p. 1.6-7.</ref>

== Materials and fire performance ==

[[Combustibility]] describes whether and how a material can burn under relevant conditions, but it does not specify a flame-spread rate by itself. Ignition response, heat capacity, decomposition and geometry all affect movement across the material. Two combustible products can therefore spread fire very differently.<ref name="Quintiere-2-247" /><ref name="Beyler-Hirschler-1-112" />

[[Reaction to fire]] testing examines product behaviour under a specified fire exposure. For flame spread, relevant observations include ignition, front movement and heat release. These describe the product in its tested configuration, whereas a spread model additionally needs the heat-transfer conditions around the advancing front.<ref name="Quintiere-2-247" /><ref name="Babrauskas-3-32">Babrauskas (2002), p. 3-32.</ref>

Surface orientation and installation affect measured performance. A product tested horizontally may not behave identically on a wall or ceiling, and joints or substrates can alter heat transfer. The tested specimen and the installed product must be compared explicitly.<ref name="Quintiere-2-247" />

A material can resist initial ignition yet still spread flame under a larger exposure. The threshold crossed in one test does not prove performance in every fire. Scenario severity and duration remain part of the assessment.<ref name="Kanury-2-231">Kanury (2002), pp. 2-231–2-232.</ref>

== Testing and measurement ==

The [[Single Burning Item test]] is described in the 2002 handbook as a European regulatory heat-release-rate test for building products. Two panels form a corner without a ceiling. This geometry differs from a complete room, so its result does not directly represent every installed exposure.<ref name="Babrauskas-3-32" />

Quintiere discusses cone-calorimeter and lateral ignition and flame-spread tests as sources of material data. These methods helped replace less meaningful flammability indices with measurements linked to ignition and spread models. They do not remove all uncertainty in heat-transfer and material-property inputs.<ref name="Quintiere-2-247" />

A spread-rate measurement needs an identifiable front, direction and exposure condition. Visible flame length alone does not establish how quickly the pyrolysis region moves. Measurement definitions can therefore change the reported result.<ref name="Quintiere-2-246" />

A room-corner test provides another configuration for interior finishes. Quintiere describes studies combining cone-calorimeter data with flame-spread models to reproduce its fire growth. The calculation still needs relationships for flame length and heat transfer in that particular geometry. Obtaining a material property in one apparatus therefore supplies part of the prediction, rather than the whole installed-product response.<ref name="Quintiere-2-254-test">Quintiere (2002), p. 2-254.</ref>

Tests at reduced scale can underrepresent radiation and room feedback. As the fire grows, upper-layer radiation and heated boundaries can preheat new regions beyond the local test arrangement. Applying small-scale rates to a developed enclosure fire requires an appropriate model.<ref name="Tien-1-73">Tien, Lee, and Stretton (2002), p. 1-73.</ref><ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

== Calculating spread and recognising its limits ==

The basic energy balance equates forward heating with the energy needed to prepare fresh material for burning. In a simplified steady model, spread speed increases when more energy reaches the fuel ahead of the front. It decreases when that fuel needs a larger temperature rise. Density and heat capacity determine how much energy the heating requires.<ref name="Quintiere-2-247" />

<math display="block">\rho V c(T_{ig}-T_s)=\dot q''</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\rho</math> || Fuel density || kg/m³
|-
| <math>V</math> || Spread speed || m/s
|-
| <math>c</math> || Specific heat capacity || kJ/(kg·K)
|-
| <math>T_{ig}</math> || Effective surface ignition temperature || °C
|-
| <math>T_s</math> || Fuel temperature ahead of the front || °C
|-
| <math>\dot q''</math> || Net heat flux preparing fresh fuel in the conceptual balance || kW/m²
|}

The temperature difference has the same numerical value in kelvin and degrees Celsius. The heat flux in this balance is the effective forward heating, rather than the fire's total heat release rate. A detailed model must establish how much energy actually reaches the fresh fuel. It must also represent the distance over which that heat acts.<ref name="Quintiere-2-247" />

For opposed-flow spread over thermally thick materials, Quintiere gives a relation fitted using lateral-spread tests. The denominator combines the material's thermal inertia with the square of the required temperature rise. The fitted parameter represents the spread conditions and fuel response. It is not a universal constant for all flows or oxygen concentrations.<ref name="Quintiere-2-250">Quintiere (2002), pp. 2-250–2-251.</ref>

<math display="block">V=\frac{\Phi}{k\rho c(T_{ig}-T_s)^2}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>k\rho c</math> || Effective thermal inertia, conductivity × density × specific heat || kW²·s/(m⁴·K²)
|-
| <math>\Phi</math> || Empirical flame-spread parameter for the material and exposure || kW²/m³
|-
| <math>V,T_{ig},T_s</math> || Spread speed and temperatures as defined above || m/s, °C, °C
|}

The test method preheats a vertical specimen by external radiation before lateral spread begins. The surface is allowed to approach a steady temperature for each exposure. The fitted properties describe that arrangement under natural convection in air. The spread relation does not calculate the preceding time needed to establish the preheated state. Downward-spread results were similar for the materials examined, except where excessive melting and dripping changed the behaviour.<ref name="Quintiere-2-250" />

For 1.27 cm Douglas fir particleboard, the handbook lists an effective ignition temperature of 382 °C. Its thermal inertia is 0.94 kW²·s/(m⁴·K²), and its spread parameter is 12.7 kW²/m³. The listed minimum surface temperature supporting continued spread is 210 °C. These are effective properties from the reported experiments, rather than universal values for all timber.<ref name="Quintiere-2-250" />

As an illustration, choose a preheated surface temperature of 250 °C, above that measured minimum. The resulting calculated spread speed is approximately 0.78 mm/s. Choosing 300 °C with the same fitted properties gives approximately 2.0 mm/s. These two chosen temperatures demonstrate the effect of preheating; they are not separate measured test results.<ref name="Quintiere-2-250" />

<math display="block">V_{250}=\frac{12.7}{0.94(382-250)^2}=0.000775\ldots\;\mathrm{m/s}\approx0.78\;\mathrm{mm/s}</math>
<math display="block">V_{300}=\frac{12.7}{0.94(382-300)^2}=0.002009\ldots\;\mathrm{m/s}\approx2.0\;\mathrm{mm/s}</math>

The relation cannot be continued without limit towards the ignition temperature. Its assumptions describe a particular spread process with fitted properties and established heating conditions. Widespread ignition, changing heat flux or a different airflow requires another treatment. Below the measured minimum temperature, continuing spread was not sustained, despite the algebraic formula still returning a positive number.<ref name="Quintiere-2-250" />

Burnout introduces a separate limitation. Fuel behind the front can finish burning while fresh material is still being heated. If spread is fast relative to burning time, the active burning area can grow; if it is slow, growth can decelerate or stop. A calculation of front speed alone therefore does not determine the complete fire's heat release.<ref name="Quintiere-2-246" />

Liquid fuels introduce an additional mechanism that the solid-material relation does not include. Surface-tension differences and circulation can transport heat within the liquid ahead of the flame. Quintiere distinguishes spread governed by this liquid motion from faster propagation through an existing flammable vapour layer. The liquid's initial temperature relative to its flash point helps distinguish these regimes.<ref name="Quintiere-2-254">Quintiere (2002), pp. 2-254–2-255.</ref>

== See also ==

* [[Euroclass system]]
* [[Travelling fire]]
* [[Trench effect]]
* [[Wildfire]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Babrauskas, V. (2002). Heat release rates. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-1–3-37). National Fire Protection Association.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Kanury, A. M. (2002). Flaming ignition of solid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-229–2-245). National Fire Protection Association.
* Quintiere, J. G. (2002). Surface flame spread. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-246–2-257). National Fire Protection Association.
* Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-73–1-89). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Ignition & Flame Spread]]

Fire triangle

2026-11-02T17:31:06Z

Peter: Improve FSE wiki article: Fire triangle; source, clarity and calculation review (GPT-6)

The '''Fire triangle''' is a simple model of three conditions needed for [[Combustion]]: fuel, oxygen and sufficient heat. Fuel is the material that can react, oxygen usually acts as the oxidiser, and heat makes ignition and continuing reaction possible. Removing or sufficiently reducing one of these conditions can prevent a fire, stop its development or contribute to extinction.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref>
[[File:fse-fire-triangle-v1.svg|thumb|upright=1.5|alt=Triangle with fuel, oxygen and heat on its three sides.|The fire triangle identifies three conditions needed for combustion. Based on Van Rossum (2027), §4.2.]]

The model is used because it connects a complex chemical and physical process with three recognisable parts of a fire scenario. It can describe a gas burner, a liquid pool or a burning solid without requiring a particular fuel geometry. It also provides a common basis for prevention and extinguishment: control the fuel, control the oxygen or control the heat.<ref name="Grant-4-152">Grant (2002), p. 4-152.</ref>

The triangle is not a complete theory of fire. It does not predict ignition time, heat release rate, flame spread or combustion products. Those outcomes also depend on mixing, heat transfer, material decomposition, geometry and changing ventilation. The model is most useful as a checklist of necessary conditions, provided these limitations remain explicit.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Drysdale-1-90">Drysdale (2002), p. 1-90.</ref>

== The three elements ==

Fuel includes more than substances supplied specifically as energy sources. Wood, paper, textiles, plastics, combustible liquids and gases can all act as fuel. Their chemical composition stores energy, while their physical form influences how that energy becomes available. Gases can mix directly with air, liquids normally evaporate first, and many solids decompose to release combustible gases.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref>

A material does not have to burn in its initial bulk form for it to be the fuel in the triangle. In a pool fire, vapour from the liquid surface takes part in flaming combustion. In a wood fire, pyrolysis produces volatile gases that can burn in a flame while residual char reacts more slowly at the surface. The original object is therefore the fuel source even though the immediate reactants change with location and time.<ref name="VR-3.1">Van Rossum (2027), §3.1.</ref><ref name="Drysdale-1-92">Drysdale (2002), p. 1-92.</ref>

Oxygen normally comes from ambient air. Van Rossum gives an approximate composition of 21% oxygen, 78% nitrogen and 1% other gases by volume. The nitrogen accompanying the oxygen absorbs part of the released energy as the gas mixture heats.<ref name="Drysdale-nitrogen">Drysdale (2002), p. 1-96.</ref> When oxygen concentration falls, combustion can become weaker and eventually stop, but the concentration at which this occurs depends on the fuel and conditions.<ref name="VR-4.2" />

Heat is the third element, but a single temperature does not describe every ignition. The fuel and oxidiser must reach a condition in which heat-producing reactions can continue despite heat losses. A flame, spark, hot surface or internal oxidation can supply the initial energy. After ignition, heat fed back from the reaction can take over from the original source.<ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

== From ignition to a self-sustaining fire ==

An [[Ignition source]] supplies local energy, but its presence alone does not establish that a self-sustaining fire will follow. The International Fire Engineering Guidelines distinguish piloted ignition of pyrolysis gases, non-piloted ignition of a sufficiently hot gas mixture and self-induced ignition driven by oxidation within a solid. Each route still requires suitable fuel and oxidiser conditions.<ref name="IFEG-2.4-4" />

For a premixed gas and air system, composition determines whether a flame can travel away from the ignition point. [[Flammability limits]] bound the concentrations within which flame propagation can be sustained under specified temperature and pressure. Beyler gives methane in air at normal temperature and pressure as an example, with lower and upper limits of 5% and 15% methane by volume. Outside this range, an ignition source can produce local burning without a flame propagating through the whole mixture.<ref name="Beyler-2-172">Beyler (2002), pp. 2-172–2-173.</ref>

These limits describe a test outcome, not merely the presence of all three elements. In the vertical-tube method described by Beyler, a mixture is ignited at the open base of a tube. The tube is 1.5 m long and 0.05 m in diameter. A mixture passes the propagation criterion if the flame travels halfway up it, beyond the immediate influence of the pilot. Igniting the same mixture at the top gives narrower limits for downward propagation. The measurement therefore needs its direction, apparatus and initial conditions as well as its fuel name.<ref name="Beyler-2-172" />

Solid and liquid fuels add a production stage before this gas-phase reaction. Heat must evaporate the liquid or decompose the solid, and the resulting vapour must mix with oxygen in suitable proportions. Some of the supplied energy is lost to surrounding materials and gases. Ignition therefore depends on the combination of energy input, exposure time, fuel properties and heat losses rather than on heat as an isolated quantity.<ref name="VR-3.1" /><ref name="Kanury-2-190">Kanury (2002), pp. 2-189–2-190.</ref>
[[File:fse-fire-triangle-v2.svg|thumb|upright=1.5|alt=Gas mixes directly, liquid evaporates and solid pyrolyses before combustion.|Fuel-state pathways to gas-phase combustion. Based on Van Rossum (2027), §4.1.]]

A self-sustaining solid-fuel fire requires continuing feedback. The flame heats unburnt fuel, that fuel releases volatile gases, and the gases maintain the flame. If the returned heat is insufficient, decomposition and flaming decline. If more fuel is heated and enough oxygen remains available, the fire can grow beyond the original ignition region.<ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

Once combustion is established, the three elements continue to interact through energy feedback. The total heat of combustion describes the energy available from complete oxidation, while heat release rate describes how quickly energy is produced. Drysdale cautions that heat-of-combustion data rarely translate directly into real-fire heat release because combustion is incomplete and burning conditions change. The triangle identifies necessary inputs but does not choose between these different quantities.<ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref>

Oxygen consumption measurements provide one way to estimate heat release during a test. The method uses the heat released per unit mass of oxygen consumed, with a correction for carbon monoxide associated with incomplete combustion. This approach depends on measuring actual oxygen use rather than assuming that all oxygen near the fuel reacts. It therefore offers a measurement framework that the conceptual triangle itself cannot supply.<ref name="Drysdale-1-96">Drysdale (2002), pp. 1-95–1-96.</ref>

Heat loss can also end combustion even when fuel and oxygen remain. Near a flammability limit, radiation and other losses can exceed heat production, preventing the flame from sustaining itself. The fire triangle should consequently be read as a dynamic balance. Removing heat can mean reducing feedback below what the reaction needs, not necessarily lowering every part of the fuel to ambient temperature.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref>

== Prevention and extinguishment ==

The triangle organises preventive measures according to the element they control. Fuel control can reduce the amount of combustible material, separate fuel from likely heat sources or change the way a material is packaged and arranged. Oxidiser control is relevant where a fuel-air mixture can be avoided or diluted. Heat control includes separating hot surfaces, flames and sparks from combustible material.<ref name="IFEG-2.4-4" /><ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref>

Fuel removal during an incident can mean stopping a gas or liquid supply, or preventing additional fuel packages from becoming involved. Cooling removes heat from the reaction zone and from fuel that would otherwise release more vapour. Limiting oxygen can suppress some fires, but this approach depends on enclosure integrity and the combustion mode. Each action addresses one side of the triangle without guaranteeing that the other conditions have become safe.<ref name="Grant-4-152" /><ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref>

[[Extinguishing mechanisms]] can therefore be understood through the same three elements, with an additional chemical mechanism represented by the fire tetrahedron. Traditional descriptions identify fuel removal, smothering and quenching as ways to interrupt combustion. Chemical inhibition instead interferes with active species in the flame. This distinction shows why the triangle explains many, but not all, extinguishing actions.<ref name="Grant-4-152" />

Smouldering illustrates why apparent removal of one element may not be enough. Oxygen can be excluded temporarily from a porous fuel bed, but hot material can react again when air returns. Ohlemiller notes that oxygen removal may need to continue until the fuel has cooled. The insulating fuel bed that supports slow combustion can also make this cooling difficult.<ref name="Ohlemiller-2-206" />

== Why the tetrahedron was added ==

The [[Fire tetrahedron]] adds the uninhibited chemical chain reaction to fuel, oxygen and heat. This extension arose from improved understanding of extinguishing agents whose action could not be explained adequately by fuel removal, oxygen limitation or cooling. Halogenated agents can remove active chemical species involved in flame reactions and thereby interrupt the reaction sequence.<ref name="Grant-4-152" />

A chain reaction includes chemical steps that produce and consume reactive species. Chain branching increases their number, while chain termination removes them. When termination dominates sufficiently, flame propagation can stop even though fuel, oxygen and a hot region remain. The fourth element consequently refers to continuation of a chemical process, not to a fourth material that must be present.<ref name="Simmons-1-150">Simmons (2002), pp. 1-150–1-151.</ref>

The tetrahedron does not make the triangle obsolete. The three original elements remain necessary for ordinary fire scenarios, and the added element clarifies why some agents work through chemistry. Both are conceptual models. Neither specifies the concentration of an extinguishing agent, the required cooling or the time needed to make a fuel bed safe.<ref name="Grant-4-152" /><ref name="Ohlemiller-2-206" />

== Fuel state and surroundings ==

The relative importance of the three elements changes with the fuel state. For a flammable gas mixture, composition and ignition energy may dominate the initial assessment. For a liquid, vapour production above the surface connects liquid temperature with the gas mixture. For a solid, thermal decomposition and heat feedback can control the continuing supply of fuel gases.<ref name="VR-4.1" /><ref name="Kanury-2-190" />

Surroundings alter all three sides. Ventilation changes oxygen supply and can remove heat and unburnt gases. Enclosure surfaces can absorb energy, while a hot upper gas layer can return radiation to fuel. Fuel geometry changes exposed area and heat losses. A complete fire description therefore places the triangle inside a defined physical setting.<ref name="VR-4.3" /><ref name="Drysdale-1-95" />

Oxygen entering a compartment does not guarantee that all fuel burns there. If fuel vapour production exceeds the air available inside, some volatiles can escape and burn after mixing with fresh air outside. The fire then remains a combustion system involving the same three elements, but the location of their combination changes. This matters when assessing where heat and flames may occur.<ref name="Drysdale-1-95" />

Scale has a similar effect on heat retention. A thin fuel layer has a large surface relative to its volume and can lose heat too rapidly for smouldering to continue. A thicker porous layer can retain heat more effectively while still admitting oxygen slowly. The three elements can be present in both cases, but only one heat balance supports sustained spread.<ref name="Ohlemiller-2-205">Ohlemiller (2002), p. 2-205.</ref>

== Using the model in fire safety work ==

During scenario development, the triangle can help document the fuel, the oxidiser and credible ignition energy separately. This makes assumptions visible and prevents attention from resting only on an ignition source while the fuel arrangement is left undefined. It also supports comparison of measures that act on different parts of the same scenario.<ref name="IFEG-2.4-4" />
[[File:fse-fire-triangle-v3.svg|thumb|upright=1.5|alt=Rows for fuel, oxygen and heat with corresponding controls.|Fire-triangle elements organise distinct control measures. Based on Grant (2002), p. 4-152 and Australian Building Codes Board et al. (2005), p. 2.4-4.]]

For flammable gases and vapours, the model leads naturally to concentration control. The 2005 guidelines describe keeping gas concentrations below the lower flammable limit as a common strategy. They caution against relying on a mixture remaining above the upper limit because dilution can bring it back into the flammable range. This is an application of fuel and oxidiser control, not an exception to the triangle.<ref name="IFEG-3.3-2" />

For solid materials, the model prompts questions about how heat reaches the fuel and how decomposition products leave it. A material's nominal presence does not describe its exposed surface, thickness, moisture or proximity to other fuel. These details influence the energy balance and must accompany any claim that a measure removes or reduces one side of the triangle.<ref name="Beyler-Hirschler-1-112">Beyler and Hirschler (2002), pp. 1-112–1-113.</ref><ref name="IFEG-2.4-4" />

In an extinguishment assessment, the model also encourages a check for reignition. Flames can disappear while hot fuel and oxygen remain available, or while a reactive region persists inside porous material. The conditions needed to prevent a visible flame are not always the same as those needed for a stable final state.<ref name="Ohlemiller-2-206" /><ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

== Limits and common misunderstandings ==

The triangle does not say that fuel, oxygen and heat must have equal importance or equal quantities. It is not a balanced chemical equation. A complete reaction specifies proportions of reactants and products, whereas the triangle only identifies conditions required for the process to operate.<ref name="Drysdale-1-92" />

The model also does not treat temperature and heat as interchangeable. Temperature describes the thermal state of a material or gas, while heat transfer delivers or removes energy over time. A small source at a high temperature can supply too little energy to ignite a large or well-cooled fuel arrangement. Conversely, internal oxidation can sometimes accumulate energy without a separate external flame.<ref name="IFEG-2.4-4" /><ref name="IFEG-3.3-2" />

Absence of visible flame does not prove that one side has been removed. Smouldering is flameless combustion at a fuel surface, and some gas-phase flames are difficult to see when little soot is produced. Evaluation therefore requires evidence about the reaction and fuel condition rather than appearance alone.<ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref><ref name="VR-4.3" />

== See also ==

* [[Ignition]]

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L. (2002). Flammability limits of premixed and diffusion flames. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-172–2-187). National Fire Protection Association.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Grant, C. C. (2002). Halon design calculations. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-149–4-172). National Fire Protection Association.
* Kanury, A. M. (2002). Ignition of liquid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-188–2-199). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-144–1-154). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Fire tetrahedron

2026-11-02T17:31:01Z

Peter: Improve FSE wiki article: Fire tetrahedron; source, clarity and calculation review (GPT-6)

The '''Fire tetrahedron''' is a conceptual model that adds the uninhibited chemical chain reaction to the fuel, oxygen and heat of the [[Fire triangle]]. It represents four conditions that support [[Combustion]] and identifies chemical inhibition as a fourth way to interrupt a fire, alongside fuel removal, oxygen limitation and cooling.<ref name="Grant-4-152">Grant (2002), pp. 4-152–4-153.</ref>
[[File:fse-fire-tetrahedron-v1.svg|thumb|upright=1.5|alt=Tetrahedron labelled fuel, oxygen, heat and uninhibited chemical chain reaction.|The fire tetrahedron adds chain chemistry to fuel, oxygen and heat. Based on Grant (2002), pp. 4-152–4-153.]]

The model developed from the observation that some extinguishing agents do not act primarily by removing fuel, excluding oxygen or absorbing heat. Halogenated agents can instead interfere with reactive chemical species in a flame. When the chain reaction can no longer sustain itself, flaming combustion stops even though the original three elements have not all been removed.<ref name="Grant-4-152" />

The tetrahedron is useful for explaining extinction and the chemistry of flames. It is not a calculation method and does not assign numerical thresholds to its four parts. Fire development still depends on material decomposition, mixing, heat transfer and the physical arrangement of fuel and oxygen.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref><ref name="Simmons-1-152">Simmons (2002), p. 1-152.</ref>

== From three elements to four ==

Fuel supplies the substance that reacts, oxygen usually serves as the oxidiser and heat enables ignition and continuing reaction. These elements explain many familiar prevention measures: keep fuel away from an ignition source, stop a fuel supply, cool burning material or restrict oxygen. They also apply to gases, liquids and solids, although liquids and solids generally need to produce vapour or decomposition gases before flaming.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref><ref name="VR-4.2">Van Rossum (2027), §4.2.</ref>

The fourth element describes how gas-phase reactions propagate through a flame. A combustion reaction is not necessarily a single direct conversion of fuel and oxygen into final products. Reactive intermediate species take part in sequences of elementary reactions. These sequences can sustain further reaction by producing additional reactive species while final combustion products and heat are formed.<ref name="Simmons-1-150">Simmons (2002), p. 1-150.</ref>

Grant explains the historical extension through the action of halons. Traditional extinguishment involved removing fuel, smothering the fire or quenching it by heat removal. Halons could instead break up the uninhibited chain reaction. The tetrahedron therefore represents a chemical route to extinction that the triangle alone did not express.<ref name="Grant-4-152" />

The geometric form is a teaching device. It does not imply that the four conditions have equal magnitudes or that a fire has four physical components. It also does not replace the need to describe the actual fuel, the oxidiser concentration or the energy supplied and lost. Its purpose is to show four places where the overall process can be interrupted.<ref name="Grant-4-152" /><ref name="Drysdale-1-90">Drysdale (2002), p. 1-90.</ref>

== Chemical chain reactions ==

A chain reaction involves reactive intermediates that are consumed in one step and regenerated in another. Chain-branching steps increase the number of these reactive centres, while chain-termination steps remove them. The balance between production and removal influences whether the reaction accelerates, reaches a steady state or dies out.<ref name="Simmons-1-150" />

One branching step in hydrocarbon flames involves a hydrogen atom reacting with an oxygen molecule to produce a hydroxyl radical and an oxygen atom. A radical is a reactive chemical species that participates in the continuing reaction sequence. In this example, one reactive centre produces two, allowing further reactions to follow. The symbols H, O₂, OH and O represent atomic hydrogen, molecular oxygen, hydroxyl and atomic oxygen respectively:<ref name="Simmons-1-149">Simmons (2002), pp. 1-149–1-150.</ref>

<math display="block">\mathrm{H}+\mathrm{O}_2\rightarrow\mathrm{OH}+\mathrm{O}</math>

Termination has the opposite effect. A hydrogen atom and a hydroxyl radical can combine to form water, removing both reactive centres. Simmons includes this recombination among the processes that limit radical concentrations in the later flame region. Branching and termination operate within the same flame, so their relative rates matter more than the presence of either reaction alone.<ref name="Simmons-1-150" />
[[File:fse-fire-tetrahedron-v3.svg|thumb|upright=1.5|alt=Reactive centre splitting into more centres or ending through termination.|Chain branching and termination influence whether reaction continues. Based on Simmons (2002), p. 1-150.]]

Simmons describes how chain branching can produce a rapid rise in reactive-centre concentration. Later consumption of reactants and termination processes limit that rise. In a hydrocarbon-air flame, these chemical developments contribute to the luminous reaction zone. The light emitted from parts of a flame can therefore be connected with excited chemical species as well as with hot particles.<ref name="Simmons-1-150" />

The chemistry varies through the flame. In a diffusion flame, fuel and oxygen arrive from different sides and react across a region with changing local composition. The fuel-rich side can be dominated by thermal decomposition and carbon formation, while the highest temperature occurs in the main reaction zone on the air side. Local reaction conditions consequently differ even when the overall fuel and oxygen amounts are known.<ref name="Simmons-1-151">Simmons (2002), pp. 1-151–1-152.</ref>

This chemical interpretation complements the physical description of mixing. In many real diffusion flames, fuel and oxygen transport controls the overall rate rather than the speed of the elementary chemical reactions. A stable flame can nevertheless depend on a small premixed region near its base, where local flow and burning velocity determine whether it remains attached or blows off.<ref name="Simmons-1-151" />

== Chemical inhibition ==

Chemical inhibition changes the balance within the reaction sequence. An inhibiting agent can remove active species or promote termination so that chain branching no longer sustains the flame. This mechanism differs from adding an inert diluent, which mainly reduces temperature and burning velocity by increasing the amount of material that must be heated.<ref name="Simmons-inhibition">Simmons (2002), pp. 1-150–1-151.</ref>

The SFPE Handbook contrasts nitrogen and bromine-containing additives to illustrate this difference. Nitrogen acts as a diluent and must be present at substantial concentration to prevent propane-air flame propagation in the reported test. Bromine compounds can be much more effective because they participate in chain-termination chemistry. The comparison belongs to the cited experiments and does not establish an agent concentration for other fuels or configurations.<ref name="Simmons-inhibition" />

Grant describes the action of Halon 1301 through bromine radicals that interfere with active flame species. The exact extinguishing mechanism was not presented as completely understood, but the chemical interaction was distinct from simple cooling or smothering. This account comes from a 2002 handbook chapter on halon design and should be read in that historical context.<ref name="Grant-4-153">Grant (2002), p. 4-153.</ref>

An [[Extinguishing agent]] that uses chemical inhibition still has to reach the reaction region in sufficient quantity and remain there under the relevant conditions. Agent movement, enclosure geometry and fire location affect this contact. The tetrahedron identifies the mechanism but does not demonstrate that a particular system will deliver the agent successfully.<ref name="Grant-4-153" />

Some fuels present additional limits. Grant lists reactive metals and substances containing their own oxidising agent among materials for which Halon 1301 was ineffective or not recommended. These examples show that interrupting one conceptual element cannot be assumed to work universally. Fuel chemistry and the location of the oxidiser can defeat an otherwise suitable mechanism.<ref name="Grant-4-152" />

== The four extinguishing routes ==

Fuel control removes or isolates the material supplying the reaction. In a continuing incident this can involve stopping a fuel flow or preventing additional items from becoming involved. In prevention it can involve reducing combustible inventory or separating fuel from energy sources. The measure acts before or during combustion by limiting what can react.<ref name="IFEG-2.4-4">Australian Building Codes Board et al. (2005), p. 2.4-4.</ref>

Oxygen limitation restricts the oxidiser reaching the reaction zone. This can be effective for some enclosed fires, but hot fuel can reignite if oxygen returns before cooling is complete. Smouldering fuels are especially relevant because their porous structure can retain heat while admitting oxygen slowly. Apparent extinction therefore has to be distinguished from a durable end to reaction.<ref name="Ohlemiller-2-206">Ohlemiller (2002), p. 2-206.</ref>

Heat removal lowers the energy available for ignition, decomposition and continuing reaction. Cooling can reduce the production of combustible vapour and weaken the feedback that sustains a flame. For a deep fuel bed, removing enough heat can be difficult because the material insulates the reaction region. The triangle's heat element therefore includes both the fire's feedback and heat losses to the surroundings.<ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref><ref name="Ohlemiller-2-206" />

[[Extinguishing mechanisms]] can use more than one route at the same time. A measure may cool the fuel while also reducing oxygen availability, while a separate agent interferes with flame chemistry. The tetrahedron does not require a measure to fit only one category. It provides language for identifying what each part of the intervention changes.<ref name="Grant-4-152" /><ref name="VR-4.3" />
[[File:fse-fire-tetrahedron-v2.svg|thumb|upright=1.5|alt=Four routes: remove fuel, limit oxygen, remove heat and inhibit chain reactions.|Four routes for interrupting combustion. Based on Grant (2002), pp. 4-152–4-153.]]

[[Flame extinction]] occurs when the flame can no longer sustain its reaction and heat balance. This can follow reduced burning velocity, excessive heat loss, lack of fuel or oxidiser, or chemical termination of the chain reaction. Extinction of visible flaming does not necessarily end smouldering or remove the possibility of later reignition.<ref name="Drysdale-1-97">Drysdale (2002), p. 1-97.</ref><ref name="Ohlemiller-2-208">Ohlemiller (2002), p. 2-208.</ref>

== Flames, heat and the chain reaction ==

The chemical chain reaction and the fire's heat balance are linked. Reactions release energy, while the temperature influences reaction rates and the stability of chemical species. Heat loss can lower temperature until propagation fails, and inhibitors can reduce reaction until heat production falls below losses. The fourth element therefore interacts with the heat element rather than operating independently.<ref name="Drysdale-1-96">Drysdale (2002), pp. 1-96–1-97.</ref>

A theoretical adiabatic flame temperature assumes no heat transfer to the surroundings. Real flames lose radiation and other energy, and high-temperature dissociation absorbs energy through changes in combustion products. These processes reduce actual temperature below a simple theoretical maximum. They also show why the tetrahedron cannot be read as four separate switches with no interaction.<ref name="Drysdale-1-96" />

Near a flammability limit, heat production and heat loss become finely balanced. Drysdale explains that radiation losses can exceed production so that a flame cannot sustain itself. Chemical inhibition can shift the same balance by lowering reaction rates. Both routes can lead to loss of flame propagation even though their physical mechanisms differ.<ref name="Drysdale-1-97" /><ref name="Simmons-1-150" />

The visible boundary of a flame is not a complete map of its chemistry. Fuel-rich and oxygen-rich regions contain different species and reaction rates, and local equilibrium assumptions can fail. Simmons notes that turbulent diffusion flames add further departures from equilibrium. This complexity is one reason the tetrahedron remains a qualitative model rather than a design equation.<ref name="Simmons-1-152" />

== Use and limits in fire safety engineering ==

The tetrahedron can support a systematic review of candidate interventions. Fuel, oxidiser, heat and reaction chemistry are considered separately, so a chemical agent is not incorrectly described as merely smothering a fire. It also encourages evaluation of whether an intervention reaches the relevant region and whether the remaining conditions permit reignition.<ref name="Grant-4-153" /><ref name="Ohlemiller-2-206" />

For a design assessment, the model must be accompanied by the fire scenario. Fuel state, ventilation, enclosure and scale determine how the four conditions develop. A flammable gas cloud, a liquid pool and a porous solid all produce different mixing and heat-transfer problems. Identical conceptual elements do not produce identical fire behaviour.<ref name="VR-4.1" /><ref name="Ohlemiller-2-201">Ohlemiller (2002), pp. 2-201–2-202.</ref>

The model is less direct for smouldering than for flaming. Smouldering is sustained by oxidation at the surface of a condensed-phase fuel and does not require a gas-phase flame. Its persistence depends strongly on oxygen transport through the fuel and heat retention. Chemical chain reactions in a flame are therefore not a sufficient description of every form of combustion.<ref name="Ohlemiller-2-200">Ohlemiller (2002), p. 2-200.</ref>

A further limitation is that thermodynamics does not determine reaction rate. Energy values can describe potential heat release, but not how quickly chemical change occurs or how a flame responds to an inhibitor. Engineering analysis combines chemical information with measured burning behaviour, flow and heat transfer rather than treating the tetrahedron as a predictive substitute.<ref name="Drysdale-1-90" />

Historical accounts of particular agents also need to be kept within their source context. The SFPE Handbook's halon chapter documents the chemistry and design understanding behind the model in 2002. It does not, by itself, establish current regulatory acceptance or suitability of that agent for a new application. The general lesson concerns interruption of reaction chemistry, not a universal recommendation of one substance.<ref name="Grant-4-152" />

The fourth element also has to be distinguished from fuel production. Pyrolysis decomposes a heated solid into smaller molecules and combustible gases without requiring oxygen at the decomposition site. Those gases may later burn through a chain reaction, but pyrolysis and combustion are separate processes. A measure can therefore reduce fuel-gas production through cooling without acting as a chemical flame inhibitor.<ref name="VR-3.1">Van Rossum (2027), §3.1.</ref>

Ignition provides another distinction. The International Fire Engineering Guidelines describe piloted, non-piloted and self-induced routes to ignition. The tetrahedron does not select between these routes or predict their timing. It becomes useful after considering whether the resulting reaction can sustain itself and which mechanism could interrupt that reaction.<ref name="IFEG-2.4-4" />

== Common misunderstandings ==

The fourth element is sometimes described as though it were another fuel component. It is instead the continuing sequence of chemical reactions that allows combustion to propagate. Fuel, oxygen and heat create conditions for that sequence, while reactive intermediates carry it forward.<ref name="Simmons-1-150" />

Removing visible flame does not demonstrate removal of all four elements. Hot fuel can remain, oxygen can return and pyrolysis gases can later form a flammable mixture. Smouldering can also continue without visible flame. A stable outcome requires assessment of the fuel condition as well as observation of the flame.<ref name="Ohlemiller-2-206" /><ref name="Ohlemiller-2-208" />

The tetrahedron does not imply that every extinguishing agent acts chemically. Fuel removal, smothering and cooling remain distinct mechanisms. Chemical inhibition is relevant when an agent changes the reaction sequence itself. Correct identification matters because delivery, persistence and fuel-specific limitations differ between these routes.<ref name="Grant-4-152" />

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Grant, C. C. (2002). Halon design calculations. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-149–4-172). National Fire Protection Association.
* Ohlemiller, T. J. (2002). Smoldering combustion. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-200–2-210). National Fire Protection Association.
* Simmons, R. F. (2002). Premixed burning. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-144–1-154). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Buoyancy

2026-11-02T17:30:18Z

Peter: Improve FSE wiki article: Buoyancy; source, clarity and calculation review (GPT-6)

'''Buoyancy''' is the upward force that arises from pressure differences around a body or fluid region immersed in another fluid. For a submerged body, Archimedes' principle relates this force to the weight of the displaced fluid. In fire safety, the term usually concerns hot combustion products that are less dense than surrounding air and therefore rise.<ref name="Kandola-1-5">Kandola (2002), pp. 1-4–1-5.</ref><ref name="VR-6.6">Van Rossum (2027), §6.6.</ref>

This upward movement drives fire plumes and contributes to smoke accumulation near ceilings. It also produces pressure differences across openings and within tall buildings. Buoyancy therefore links fire temperatures with smoke transport, ventilation flows and the exposure of spaces away from the fire.<ref name="IFEG-2.5-2">Australian Building Codes Board et al. (2005), p. 2.5-2.</ref><ref name="IFEG-2.5-6">Australian Building Codes Board et al. (2005), p. 2.5-6.</ref>

Buoyancy is not the same as convection. It is a driving force, while convection is heat transfer associated with moving gas or liquid. Buoyant motion can transport energy and combustion products, but wind, fans and other pressure differences can change the resulting flow.<ref name="VR-5.3">Van Rossum (2027), §5.3.</ref>

== Pressure, displacement and density ==

Pressure in a static fluid changes with height because of the weight of fluid above. A submerged body experiences different pressures on its upper and lower surfaces. The vertical difference between the resulting pressure forces produces an upward buoyant force.<ref name="Kandola-1-4">Kandola (2002), p. 1-4.</ref>
[[File:fse-buoyancy-v1.svg|thumb|upright=1.5|alt=Less dense hot gas rising through denser cool gas under pressure differences.|Density contrast produces buoyancy in hot fire gases. Based on Kandola (2002), pp. 1-4–1-5 and Van Rossum (2027), §3.2.]]

Archimedes' principle states that the lifting force equals the weight of the displaced fluid volume. If this force exceeds the body's weight, the body rises or floats. If it is smaller, the body sinks. Equilibrium requires the appropriate balance of forces and, for rotational stability, a suitable relationship between the centres of gravity and buoyancy.<ref name="Kandola-1-5" />

The centre of buoyancy is located at the centroid of the displaced fluid volume. This geometric result helps explain why shape and orientation affect stability. It is separate from the centre of gravity, where the body's weight acts.<ref name="Kandola-1-5" />

For hot gases, a simple displaced-body picture becomes part of a wider flow. The heated region is not a sealed object moving through still air. It expands, mixes and exchanges heat while pressure and density vary around it. The same density principle nevertheless explains the upward driving force.<ref name="VR-6.6" /><ref name="Atreya-1-44">Atreya (2002), p. 1-44.</ref>

Density differences, rather than temperature alone, provide the direct mechanical contrast. Heating usually lowers gas density at approximately constant pressure, but composition and pressure also affect density. A complete flow assessment therefore avoids treating temperature as a direct velocity or force without the intervening physics.<ref name="VR-3.2">Van Rossum (2027), §3.2.</ref>

== Heating and the ideal-gas relationship ==

The [[Ideal gas law]] connects pressure, volume, temperature and amount of gas. At approximately constant pressure, heating allows a given mass of gas to occupy more volume, reducing its density. If volume cannot change freely, pressure can instead increase. These alternatives shape different enclosure scenarios.<ref name="VR-3.2" />

Absolute temperature in kelvin is required for this relationship. Van Rossum gives an approximation for air density near atmospheric pressure, yielding about 1.2 kg/m³ at 20 °C and 0.75 kg/m³ at 200 °C. The example shows why hot combustion products tend to rise through cooler air.<ref name="VR-3.2" />

These values are not a general smoke-density table. Real smoke contains entrained air and combustion products whose temperature and composition change. The approximation is useful for illustrating density, but an engineering calculation needs conditions appropriate to the actual gas.<ref name="VR-3.2" /><ref name="IFEG-2.5-2" />

=== A simple pressure calculation ===

A column of gas has weight, so its pressure decreases with height. Two columns with different densities have different rates of pressure decrease. If their pressures are equal at a reference height, a pressure difference develops above or below that level. Van Rossum gives the following approximation for uniform warm and cool columns.<ref name="VR-3.2" />

<math display="block">\rho\approx\frac{353}{T},\qquad \Delta p\approx g h(\rho_c-\rho_h)</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\rho</math> || Approximate air density near atmospheric pressure || kg/m³
|-
| <math>T</math> || Absolute gas temperature || K
|-
| <math>\Delta p</math> || Warm-column pressure minus cool-column pressure above an equal-pressure reference level || Pa
|-
| <math>g</math> || Gravitational acceleration || m/s²
|-
| <math>h</math> || Height above the reference level || m
|-
| <math>\rho_c,\rho_h</math> || Cool and hot column densities || kg/m³
|}

The coefficient 353 is used with temperature in kelvin to obtain density in kilograms per cubic metre. It incorporates the assumed gas properties and atmospheric pressure. The pressure expression assumes each column has approximately constant density over the height considered. It describes the buoyant contribution before wind, ventilation and flow resistance are included.<ref name="VR-3.2" />

For an illustrative calculation, consider air columns at Van Rossum's example temperatures of 20 °C and 200 °C. Choose a height of 3 m above a level where their pressures are equal. This height is an example assumption, not a prescribed building dimension. Using 9.8 m/s² for gravitational acceleration follows the value in the 2005 International Fire Engineering Guidelines.<ref name="VR-3.2" /><ref name="IFEG-2.5-6" />

The temperatures become 293.15 K and 473.15 K, giving densities of approximately 1.20 kg/m³ and 0.746 kg/m³. Keeping the unrounded densities in the calculation gives about 13.5 Pa. At the upper level, pressure in the hotter column exceeds pressure in the cooler column. The difference arises because pressure falls less rapidly with height in the less dense gas.<ref name="VR-3.2" />

<math display="block">\Delta p\approx9.8\times3\times\left(\frac{353}{293.15}-\frac{353}{473.15}\right)\approx13.5\ \mathrm{Pa}</math>

This result is a pressure estimate, not a smoke velocity or exhaust capacity. Turning pressure into a flow rate also requires the opening geometry and flow resistance. An actual building's equal-pressure level depends on its openings and other driving forces. The chosen reference level cannot simply be assumed for every room or shaft.<ref name="IFEG-2.5-6" /><ref name="VR-3.2" />

Heating also causes expansion. When a room cannot accommodate the increased gas volume, gas is pushed through available openings. Van Rossum notes that this can become pronounced around flashover, forcing hot gases through seams, cracks and holes as well as larger vents.<ref name="VR-6.6" />

Expansion and buoyancy should be distinguished. Expansion results from increasing gas volume or pressure, while buoyancy results from density contrasts and gravity. Both can act during the same fire and contribute to flow through different parts of an opening.<ref name="VR-6.6" />

== Fire plumes and entrainment ==

A [[Fire plume]] is the rising flow of hot combustion products above a fire. Buoyancy drives the upward motion, and turbulence draws surrounding air into the plume. The plume widens and becomes more diluted as its mass flow increases.<ref name="VR-5.3" /><ref name="VR-6.7">Van Rossum (2027), §6.7.</ref>
[[File:fse-buoyancy-v2.svg|thumb|upright=1.5|alt=Fire plume entraining air as it rises and spreads beneath a ceiling.|Buoyancy drives plume rise and upper-layer formation. Based on Van Rossum (2027), §6.7 and Australian Building Codes Board et al. (2005), p. 2.5-2.]]

This air entrainment can greatly exceed the mass flow of burned fuel. The 2005 International Fire Engineering Guidelines note that some smoke-development methods consequently neglect the fuel mass flow in comparison. Heat release from the fuel still establishes the buoyant source, so neglecting its mass is not the same as neglecting the fire.<ref name="IFEG-2.5-2" />

The plume transports heat as well as combustion products. Its temperature and concentration decline through dilution and heat exchange, while the total volume of affected gas increases. A relatively small fire can therefore create a large smoke flow.<ref name="VR-5.3" />

Plume geometry affects entrainment. The 2005 guidelines describe axisymmetric models for fires away from walls, where air can enter from all sides. Walls, corners and obstructions alter this symmetry and require suitable models rather than an unmodified free-plume assumption.<ref name="IFEG-2.5-2" />

Different plume regions can also behave differently. The guidelines refer to persistent-flame, intermittent-flame and buoyant-plume regions in one modelling approach. A single velocity or temperature should therefore not be assumed to represent the entire height from fuel surface to ceiling.<ref name="IFEG-2.5-2" />

== Hot layers and stratification ==

When a rising plume reaches the top of an enclosure, smoke spreads beneath the ceiling and can form a [[Hot gas layer]]. Sufficient temperature contrast between the plume and room air supports a stratified situation, with hotter gas above cooler gas. Weak contrast and strong mixing can instead produce more homogeneous conditions.<ref name="VR-6.7" />

The layer accumulates mass and energy supplied by the plume. Its depth and temperature influence radiation to lower objects, heat transfer to boundaries and flow through openings. Buoyancy therefore affects the enclosure even after the initial vertical rise has ended.<ref name="VR-6.7" /><ref name="IFEG-2.5-2" />

The upper layer is not composed only of products generated directly by combustion. Entrained air forms much of its volume, and this dilution changes density and composition. Layer buoyancy depends on the resulting mixture, not on flame temperature alone.<ref name="VR-5.3" /><ref name="IFEG-2.5-2" />

At an opening, the [[Neutral plane]] marks the height around which the pressure relationship changes and flow can reverse direction. The 2005 guidelines explain that its location is often near, but not identical to, the smoke-layer interface. A lower smoke interface therefore does not necessarily place the neutral plane at the same height.<ref name="IFEG-2.5-6" />

Neutral-plane and layer-interface positions should therefore not be treated as interchangeable definitions. One concerns pressure-driven flow, while the other describes a smoke concentration or thermal region. Their relationship depends on the enclosure and opening conditions.<ref name="IFEG-2.5-6" />

== Stack effect and vertical shafts ==

[[Stack effect]] is buoyancy-induced pressure difference caused by temperature differences between the inside and outside of a building, particularly over tall vertical spaces. Elevator shafts, stairwells and service ducts can provide routes for the resulting vertical smoke movement.<ref name="IFEG-2.5-6" /><ref name="VR-6.6" />
[[File:fse-buoyancy-v3.svg|thumb|upright=1.5|alt=Tall shaft with upward smoke and an opening with opposing flows around a neutral plane.|Stack effect and neutral-plane exchange shape smoke movement. Based on Australian Building Codes Board et al. (2005), p. 2.5-6.]]

A chimney can strengthen vertical flow by limiting horizontal mixing. Van Rossum notes that the effect can also occur without a chimney wherever density differences act over height. Architectural form changes the flow but does not create the underlying thermal principle.<ref name="VR-6.6" />

Stack effect can move smoke in directions that a local plume description would not predict. It can draw gas upwards through remote shafts or contribute to exchange through openings at different heights. The direction depends on inside-outside temperature and pressure distributions.<ref name="IFEG-2.5-6" />

Wind adds another pressure field, and mechanical systems can add or remove air at selected locations. These forces can strengthen, weaken or reverse buoyancy-driven flow. A smoke assessment based only on hot gas rising in still air can therefore miss important paths.<ref name="VR-6.6" />

Openings themselves modify flow. Discharge coefficients, effective area and unsteady exchange can affect how much gas crosses. The 2005 guidelines note puffing and exchange flow through horizontal vents, demonstrating that an opening is not a simple passive hole in every configuration.<ref name="IFEG-2.5-7">Australian Building Codes Board et al. (2005), p. 2.5-7.</ref>

== Buoyancy and convective heat transfer ==

[[Convection]] uses the moving gas to transport energy. Buoyancy supplies one means of motion, while forced convection uses external influences such as wind or fans. In many fires both occur together as mixed convection.<ref name="VR-5.3" /><ref name="Atreya-1-44" />

The convective energy carried by a flow depends on its temperature, density, specific heat and volume flow. Buoyancy influences these variables indirectly by driving entrainment and transport. It does not by itself specify the watts delivered to a surface.<ref name="VR-5.3" />

At walls and ceilings, boundary-layer flow controls heat exchange between gas and solid. The same buoyant movement that brings hot gas to a surface therefore produces a second heat-transfer problem at that surface. Plume transport and surface heat flux require different analyses.<ref name="VR-5.3" />

[[Smoke movement]] includes the wider result of buoyancy, expansion, wind and equipment acting through the building. It includes gas composition and visibility as well as heat. Buoyancy is fundamental to many smoke scenarios, but it is only one component of the complete pressure and transport model.<ref name="VR-6.6" />

== Buoyancy and smoke management ==

Smoke-management methods work with or against the pressure and density conditions created by fire. The 2005 International Fire Engineering Guidelines identify natural ventilation, zone pressurisation, extraction, dilution and containment as broad approaches. Each changes the flow path or the accumulation of smoke in a different way.<ref name="IFEG-2.5-7" />

Natural ventilation uses openings to release hot smoke and admit replacement air. Buoyancy can provide much of the driving force, but vent location and area determine how that force produces flow. Wind can alter the intended direction and must be considered where it affects the system.<ref name="IFEG-2.5-6" /><ref name="VR-6.6" />

Zone pressurisation establishes a pressure difference intended to keep selected spaces clear of smoke. This approach can oppose buoyancy-driven movement across a boundary. Its effect depends on maintaining the required pressure relationship when doors, vents and other openings change state.<ref name="IFEG-2.5-7" /><ref name="VR-6.6" />

Extraction removes smoke and its transported energy from the building. It can reduce accumulation while also changing the pressure field and air entrainment into the fire region. The exhaust flow and make-up air therefore have to be considered together with the buoyant source.<ref name="VR-5.3" /><ref name="IFEG-2.5-7" />

Dilution adds air to reduce smoke concentration, but it changes the total gas flow and does not remove the fire's heat source. Containment instead limits the region through which smoke can travel. Both approaches still require an account of buoyancy at openings and within vertical spaces.<ref name="IFEG-2.5-7" /><ref name="IFEG-2.5-6" />

These methods demonstrate why buoyancy is not simply a reason for smoke to rise unimpeded. It is one force within a designed and changing system. Effective analysis identifies the intended pressure and flow pattern, then tests whether fire, wind and equipment can maintain or disturb it.<ref name="VR-6.6" />

== Engineering use and uncertainty ==

Buoyancy-informed models estimate plume mass flow, smoke production, layer conditions and vent flow. Their inputs include heat release rate, geometry, gas properties and opening arrangements. Results must be tied to the model's applicable fire size and position.<ref name="IFEG-2.5-2" />

A free-plume result should not be transferred automatically to a wall or corner fire. Likewise, a stratified-layer model should not be used where mixing has removed the assumed layer. Checking these physical assumptions is as necessary as selecting correct numerical values.<ref name="VR-6.7" /><ref name="IFEG-2.5-2" />

Time changes the force and the flow. Heat release rate, smoke temperature, vent state and mechanical-system operation can all vary. A steady buoyancy calculation can represent selected conditions but does not establish the complete sequence of smoke spread.<ref name="VR-5.1">Van Rossum (2027), §5.1.</ref><ref name="VR-6.6" />

Rising hot gas does not mean every particle moves only upwards. Turbulence, obstacles, wind and pressure differences create horizontal and downward components. A building-scale assessment follows the resulting flow field rather than relying on the simplified image of a vertical column.<ref name="IFEG-2.5-6" /><ref name="VR-5.3" />

Field interpretation needs corresponding measurements of temperature, pressure and flow. Temperature helps establish density, pressure differences help establish driving force and opening conditions reveal the resulting transport. None of these observations alone describes the entire buoyant system.<ref name="Kandola-1-4" /><ref name="IFEG-2.5-6" />

== See also ==

* [[Vent flow]]

== Notes ==

<references />

== References ==

* Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Kandola, B. S. (2002). Introduction to mechanics of fluids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-1–1-26). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Physics & Heat Transfer]]

Flash point

2026-11-02T17:29:08Z

Peter: Improve FSE wiki article: Flash point; source, clarity and calculation review (GPT-6)

'''Flash point''' is the lowest liquid temperature producing a momentary flash above its surface when a pilot flame is applied in a specified test. It describes a response of the vapour mixture, not the temperature at which the entire liquid must burn continuously.<ref name="Kanury-2-190">Kanury (2002), p. 2-190.</ref>

The property is used as an indicator of how readily a liquid can produce an ignitable vapour mixture. A lower flash point generally corresponds to greater volatility under comparable conditions, but the measured value depends on the apparatus and procedure. Open-cup and closed-cup results are not automatically interchangeable. The reported method forms part of the result and must remain attached to the numerical value.<ref name="Kanury-2-190" />

Flash point must be distinguished from fire point and autoignition temperature. At fire point, burning continues rather than flashing and ceasing. Autoignition occurs without a local pilot when the mixture is sufficiently hot. These distinctions make flash point useful for fire prevention while limiting its ability to describe a developed fire.<ref name="Kanury-2-190" />

== Vapour production and flammability ==

A liquid does not usually undergo flaming combustion throughout its bulk. Heat causes evaporation at the surface, and the vapour mixes with air above the liquid. Flaming occurs in this gas mixture when composition, temperature and ignition conditions are suitable. Sustained burning then depends on continued vapour production and heat feedback to the liquid.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref><ref name="Kanury-2-189">Kanury (2002), pp. 2-189–2-190.</ref>

[[Flammability limits]] define the fuel concentrations between which a premixed flame can propagate under stated conditions. The lower limit is the lean side, with relatively little fuel vapour, and the upper limit is the rich side. Flash point is related to the temperature needed to establish an ignitable mixture near the liquid surface, but it is a test property rather than a direct concentration measurement.<ref name="Kanury-2-190" /><ref name="Beyler-2-172">Beyler (2002), pp. 2-172–2-173.</ref>

Beyler illustrates flammability with methane in air, which propagates flame between 5% and 15% methane by volume at normal temperature and pressure. A local pilot can cause combustion outside such limits without producing a flame that travels through the wider mixture. This distinction between local ignition and propagation is central to the flash-point test.<ref name="Beyler-2-172" />

Vapour pressure links liquid temperature with the amount of vapour available, but the mixture above a real liquid is also affected by air movement and container geometry. Kanury notes that the vapour concentration above a vaporising surface depends on physical transport as well as fuel properties. Flash point therefore cannot be inferred from boiling point alone.<ref name="Kanury-2-189" />

The surrounding pressure and oxygen concentration also matter. Flammability limits are specified at particular temperature and pressure, and changes in inert gas concentration alter the mixture. A tabulated flash point consequently describes standardised test conditions rather than every storage or process environment.<ref name="Beyler-2-172" /><ref name="Kanury-2-190" />

== How the test works ==

In the definition used by Kanury, the liquid is presumed to have a uniform temperature. A small gas-flame pilot makes a quick sweep near the vaporising surface. The observed result is a momentary flame propagation through the vapour-air layer. Sustained burning is not required for the flash-point observation.<ref name="Kanury-2-190" />
[[File:fse-flash-point-v1.svg|thumb|upright=1.5|alt=Open and closed cups with vapour above liquid and a pilot sweeping near the surface.|Flash-point tests use a pilot and a defined cup configuration. Based on Kanury (2002), pp. 2-190–2-191.]]

Closed-cup apparatus retains vapour more effectively and limits disturbance by room air currents. Open-cup apparatus exposes the sample more directly to its surroundings. Kanury reports that closed-cup methods, such as Pensky-Martens, generally produce flashing at a lower temperature than open-cup methods, such as Cleveland, in the cited comparisons.<ref name="Kanury-2-190" />

The difference between methods is not always small or systematic. Table 2-8.1 lists naphtha at 34.4 °C in the Abel test and 50.0 °C in the Luchaire test. Kerosene is 52.8 °C by Abel and 60.0 °C by Cleveland. These examples demonstrate why a result needs its method, rather than serving as a universally interchangeable material constant.<ref name="Kanury-2-191">Kanury (2002), p. 2-191.</ref>

Cup walls, airflow, heat transfer and vapour leakage all influence the observed flash. Closed cups reduce alterations caused by drafts, while still allowing limited air leakage into the test region. Conductive cup walls and the location of the pilot also affect the mixture and its heating. The measurement is therefore an operational property tied to a defined procedure.<ref name="Kanury-2-191" />

== Flash point, fire point and autoignition ==

At flash point, the applied pilot can produce a flame that flashes through the available mixture and then goes out. The vapour production rate is not yet sufficient for self-sustained burning under the test conditions. This is why the term should not be used as a synonym for the start of every liquid fire.<ref name="Kanury-2-190" />
[[File:fse-flash-point-v2.svg|thumb|upright=1.5|alt=Three panels: flash then out, sustained flame and self-ignition without pilot.|Flash point, fire point and autoignition describe different observations. Based on Kanury (2002), p. 2-190.]]

Fire point is defined similarly except that the flame must continue and sustain burning of the liquid. Continued heat feedback and vapour production are now sufficient. Table 2-8.2 gives open-cup flash/fire-point pairs of 92/97 °C for Texas solar oil and 133/164 °C for fuel oil. Their respective differences are 5 °C and 31 °C, demonstrating that no fixed temperature increment converts flash point to fire point.<ref name="Kanury-2-190" /><ref name="Kanury-2-191" />

[[Autoignition temperature]] is the minimum temperature at which a vapour or gas mixture with air ignites without a local pilot. The test can involve a heated flask, furnace, bomb, compression device or hot surface. Autoignition also involves ignition delay, so the observed response depends on exposure and method.<ref name="Kanury-2-189" />

A liquid can have a low flash point and a much higher autoignition temperature because the two tests ask different questions. Flash point concerns the availability of an ignitable mixture for a pilot. Autoignition concerns whether the mixture can begin reacting without that pilot. Neither value alone describes all possible [[Ignition]] routes.<ref name="Kanury-2-190" />

The 2005 International Fire Engineering Guidelines list acetone with a flash point of −18 °C and an autoignition temperature of 465 °C, and ethanol with corresponding values of 13 °C and 365 °C. Methanol is listed at 11 °C and 470 °C. These older tabulated values illustrate the distinction, but their source and test basis must accompany any application.<ref name="IFEG-3.3-3">Australian Building Codes Board et al. (2005), pp. 3.3-2–3.3-3.</ref>

== Flash point in liquid-fire development ==

A [[Pool fire]] requires continuing evaporation from the liquid surface and combustion of the resulting vapour. Heat from the flame returns to the liquid, supporting further vapour production. Flash point can indicate whether a piloted flash is possible at a lower liquid temperature, but it does not determine the later heat release rate or size of this developed fire.<ref name="VR-4.1" /><ref name="Kanury-2-190" />

Before a sustained pool fire develops, vapour may accumulate or disperse according to ventilation and container geometry. A spill in still air and a spill exposed to strong airflow can produce different local concentrations at the same liquid temperature. The relevant question is therefore whether an ignitable mixture occurs where an ignition source is present.<ref name="Kanury-2-189" /><ref name="IFEG-3.3-2">Australian Building Codes Board et al. (2005), p. 3.3-2.</ref>

The 2005 guidelines explain that liquid fuels present a safety issue similar to gases when enough vapour enters the flammable range. Very low-energy ignition sources can then be sufficient. Their preventive strategy for gases and vapours is to keep concentrations below the lower flammable limit, rather than relying on a rich mixture remaining above the upper limit after dilution.<ref name="IFEG-3.3-2" />

Flash point can support this assessment by showing how liquid temperature affects vapour availability under the test method. It does not measure vapour concentration at a particular distance from a spill, nor the ignition energy of that mixture. Those quantities require separate information about the scenario.<ref name="Kanury-2-190" /><ref name="Beyler-2-172" />

== Use in prevention and classification ==

For [[Hazardous area classification]], flash point supplies information about the liquid rather than the extent of a flammable atmosphere. The underlying ignition issue is whether released vapour mixes with air within its flammable range. This requires information about the release and mixing conditions as well as the liquid property.<ref name="IFEG-3.3-2" />

For storage and handling, a lower flash point signals that an ignitable vapour mixture can develop at a lower liquid temperature under comparable conditions. Control can therefore address liquid temperature, vapour accumulation and ignition sources together. The fire-triangle elements remain separate even though flash point combines their effects in one test observation.<ref name="VR-4.2">Van Rossum (2027), §4.2.</ref><ref name="Kanury-2-190" />

The property is also useful when comparing liquids through consistent data. Comparisons should use the same method and edition of the source, with units and any pressure conditions retained. Mixing an open-cup value for one liquid with a closed-cup value for another can distort the comparison.<ref name="Kanury-2-191" />

Flash point is not a measure of toxic hazard, soot production or total chemical energy. It does not state how much fuel is present or how fast it will burn after sustained ignition. Those aspects need combustion, toxicity and fire-scenario data rather than a single ignition-related temperature.<ref name="Drysdale-1-95">Drysdale (2002), p. 1-95.</ref><ref name="VR-4.5">Van Rossum (2027), §4.5.</ref>

== Comparing liquids and source data ==

A meaningful comparison starts with values obtained on the same basis. The 2005 International Fire Engineering Guidelines place flash point beside flammability limits, autoignition temperature and boiling point for common gases and vapours. This arrangement helps distinguish the properties, but does not imply that one can be calculated reliably from another without a suitable model and conditions.<ref name="IFEG-3.3-3" />

The table gives benzene a flash point of −11 °C, toluene 4 °C, styrene 31 °C and decane 46 °C. These are the temperatures reported by that compilation; the table does not identify the cup method for each entry. They do not rank the later heat release rates or total hazards of fires involving these liquids.<ref name="IFEG-3.3-3" />
[[File:fse-flash-point-v3.svg|thumb|upright=1.5|alt=Flash points: benzene minus 11, toluene 4, styrene 31 and decane 46 °C.|Selected flash points tabulated in the 2005 IFEG. Based on Australian Building Codes Board et al. (2005), pp. 3.3-2–3.3-3.]]

The same source lists lower and upper flammability limits alongside these temperatures. Benzene has listed limits of 1.3% and 7.9% by volume, while ethanol has 3.3% and 19%. Such data describe gas-mixture composition, whereas flash point describes liquid temperature in a particular apparatus. Keeping the quantities separate prevents a temperature from being mistaken for a vapour concentration.<ref name="IFEG-3.3-3" />

Kanury's multi-method table provides a second kind of comparison. Gas oil is listed at 90.6 °C by Pensky-Martens, 93.3 °C by Cleveland and 92.2 °C by Luchaire. The pattern across methods is not sufficiently consistent to support one universal correction between all tests.<ref name="Kanury-2-191" />

Heavier fuels tending to have higher flash points in these data is an observed trend, not a substitute for measurement. Kanury also notes that several trends across fuel families are weak or conceptually uncertain. A liquid's name or broad family therefore does not justify inventing a value when a tested result is unavailable.<ref name="Kanury-2-190" />

Source age and scope also matter. The SFPE Handbook chapter dates from 2002 and the guidelines from 2005. Their values record the results assembled in those editions. In particular, the IFEG table does not identify a cup method for each flash point. Its entries cannot establish method-specific classification boundaries without that missing information.<ref name="Kanury-2-191" /><ref name="IFEG-3.3-3" />

== Vapour concentration and a worked example ==

A simple evaporation model explains why flash point depends on both temperature and mixing. It first estimates the equilibrium vapour concentration immediately at the liquid surface. It then distinguishes that value from the concentration where the pilot passes. Kanury presents this approach as a physical explanation with significant predictive limitations.<ref name="Kanury-2-194">Kanury (2002), pp. 2-194–2-195.</ref>

At normal atmospheric pressure, the surface vapour fraction can be estimated from the liquid's normal boiling point and enthalpy of vaporisation. The latter is the energy needed to evaporate unit mass of liquid. The equation assumes ideal-gas behaviour, equilibrium at the surface and an approximately constant enthalpy of vaporisation. Temperatures in this equation are absolute temperatures in kelvin.<ref name="Kanury-2-194" />

<math display="block">x_s=\frac{p_{v,s}}{p_0}=\exp\left[\frac{h_{fg}}{R T_b}\left(1-\frac{T_b}{T_s}\right)\right]</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>x_s</math> || Mole fraction of fuel vapour at the surface || Dimensionless
|-
| <math>p_{v,s}</math> || Equilibrium vapour pressure at the surface || Pa
|-
| <math>p_0</math> || Atmospheric pressure at the normal boiling point || Pa
|-
| <math>h_{fg}</math> || Enthalpy of vaporisation, approximated by its normal-boiling-point value || kJ/kg
|-
| <math>R</math> || Specific gas constant of the fuel vapour || kJ/(kg·K)
|-
| <math>T_b</math> || Normal boiling temperature || K
|-
| <math>T_s</math> || Liquid surface temperature || K
|}

For ethanol, Kanury's table gives a normal boiling temperature of 351 K and an enthalpy of vaporisation of 837 kJ/kg. Its molecular mass is 46 kg/kmol. Dividing the universal gas constant, 8.314 kJ/(kmol·K), by that molecular mass gives the specific gas constant used below.<ref name="Kanury-2-192">Kanury (2002), p. 2-192, Table 2-8.4.</ref><ref name="Kanury-2-194" />

Take a surface temperature of 286 K, the closed-cup flash point listed in the same table. Substitution gives a surface vapour fraction of approximately 0.050, or 5.0% by volume. The unrounded values are retained during the calculation. This result estimates the surface concentration under the model assumptions; it does not independently predict the measured flash point.<ref name="Kanury-2-192" /><ref name="Kanury-2-194" />

<math display="block">R=\frac{8.314}{46}=0.180739\ldots\;\mathrm{kJ/(kg\,K)}</math>
<math display="block">x_s=\exp\left[\frac{837}{(8.314/46)\times351}\left(1-\frac{351}{286}\right)\right]\approx0.050</math>

The same source lists ethanol's lean flammability limit as a volume fraction of 0.033. Above the surface, dilution and transport reduce the fuel concentration relative to its equilibrium surface value. The mixture at the pilot may therefore differ substantially from the calculated 5.0%. Its location and application time remain part of the experiment.<ref name="Kanury-2-192" /><ref name="Kanury-2-194" />

Kanury represents this reduction by a dimensionless transport factor smaller than unity. A propagating flash requires enough fuel at the pilot, together with an effective pilot and suitable thermal conditions. A model using only the surface value omits that transport problem. It also does not resolve the full energy balance or the empirical dependence of flammability limits on the apparatus.<ref name="Kanury-2-194" />

These limitations explain why a boiling point cannot be converted directly into a reliable flash point. They also explain why a temperature below one reported cup-test result does not describe every possible release configuration. Flash point characterises the specified test, while fire development additionally depends on vapour supply, fuel inventory and heat feedback.<ref name="Kanury-2-189" /><ref name="Kanury-2-194" /><ref name="VR-4.5" />

== Notes ==

<references />

== References ==

* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L. (2002). Flammability limits of premixed and diffusion flames. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-172–2-187). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Kanury, A. M. (2002). Ignition of liquid fuels. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-188–2-199). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

Conduction

2026-11-02T17:29:03Z

Peter: Improve FSE wiki article: Conduction; source, clarity and calculation review (GPT-6)

'''Conduction''' is heat transfer through molecular interactions within a material or between materials in contact. Energy diffuses from a higher-temperature region to a lower-temperature region without requiring the bulk material to move with it. In buildings, conduction is particularly relevant to heat travelling through walls, floors, roofs and structural members.<ref name="VR-5.2">Van Rossum (2027), §5.2.</ref><ref name="Rockett-Milke-1-28">Rockett and Milke (2002), p. 1-28.</ref>

A fire can heat one side of a construction while the other side remains comparatively cool. Conduction through the construction then raises the temperature of the cooler side and can expose people, combustible contents or structural material there. The process also removes heat from hot smoke and flames into surrounding boundaries.<ref name="VR-5.2" /><ref name="IFEG-2.6">Australian Building Codes Board et al. (2005), pp. 2.6-2, 2.6-6.</ref>

The rate of conduction depends on temperature difference, material properties, thickness, area and time. A steady calculation assumes temperatures no longer change, whereas a real fire produces changing surface and internal temperatures. Both views are useful, but they answer different questions.<ref name="VR-5.1">Van Rossum (2027), §5.1.</ref><ref name="Rockett-Milke-1-29">Rockett and Milke (2002), p. 1-29.</ref>

== How energy moves through a solid ==

Conduction occurs through microscopic energy transfer. In good electrical conductors, free electrons make an important contribution. In electrical insulators, lattice vibrations called phonons still allow substantial heat conduction. Imperfections scatter these carriers and diffuse their energy through the solid.<ref name="Rockett-Milke-1-28" />

The direction of net heat flow is from hot to cold. A larger temperature gradient, meaning a larger temperature change over a given distance, drives more conductive heat flow under otherwise equal conditions. Cross-sectional area also matters because a larger area provides more parallel routes for energy transfer.<ref name="Rockett-Milke-1-28" />
[[File:fse-conduction-v1.svg|thumb|upright=1.5|alt=Hot wall surface transferring energy through stationary material to the cool side.|Conduction transfers energy through a stationary solid. Based on Rockett and Milke (2002), p. 1-28.]]

Conduction does not require a visible opening or a flowing fluid. A continuous solid can transmit heat across its thickness even when it prevents smoke from passing. This makes conductive exposure different from direct flame contact and from smoke movement through gaps.<ref name="VR-5.2" />

Heat can also be conducted within gases and liquids, although fire assessments often emphasise movement of those fluids as well. At a stationary surface, the fluid immediately adjacent to it has little or no bulk velocity, so molecular transfer remains part of the surface heat-exchange process.<ref name="VR-5.2" /><ref name="Atreya-1-44">Atreya (2002), p. 1-44.</ref>

== Conductivity, heat capacity and diffusivity ==

[[Thermal conductivity]] expresses how readily a material conducts heat. A higher conductivity allows more heat flow for the same temperature difference, thickness and area. It is commonly expressed in watts per metre-kelvin, linking heat flow with distance and temperature difference.<ref name="VR-5.2" /><ref name="Rockett-Milke-1-28" />

Conductivity is not necessarily constant. Temperature, moisture and changes within the material can alter its thermal response; processing can also change conductivity. Some laminates, fibrous materials and reinforced products also conduct differently along and across their grain or layers. Such materials require direction-specific properties rather than one assumed value in every direction.<ref name="Rockett-Milke-1-28" /><ref name="VR-5.2" />

[[Specific heat capacity]] describes how much energy is needed to raise a unit mass by one degree. It affects how much thermal energy a material stores while its temperature rises. Conductivity concerns transmission through the material, while heat capacity concerns storage within it.<ref name="Rockett-Milke-1-29" /><ref name="Drysdale-1-91">Drysdale (2002), p. 1-91.</ref>

[[Thermal diffusivity]] combines conductivity, density and specific heat capacity. It describes how quickly a temperature disturbance can propagate through a material by conduction. Rockett and Milke identify square metres per second as its unit. A high diffusivity does not mean that the material stores more heat; it means that temperature changes penetrate more readily.<ref name="Rockett-Milke-1-29" />

The distinction matters during a fire. One construction may accept heat slowly at its surface but transmit temperature changes efficiently, while another stores considerable energy near the exposed side. Material selection therefore needs more than a single conductivity value when transient exposure is assessed.<ref name="Rockett-Milke-1-29" />

== Thickness, layers and thermal resistance ==

For a uniform layer under steady, one-dimensional conditions, a thicker layer provides more resistance to heat flow. Van Rossum explains that doubling thickness doubles this resistance when conductivity remains unchanged. Doubling conductivity instead halves the resistance. These relationships describe the simplified steady model, not every transient fire exposure.<ref name="VR-5.2" />

Thermal resistance offers a convenient way to describe several layers in series. Heat passing from one side of a composite construction to the other crosses each layer in turn. Under the steady model, the resistances of the layers can be added, just as electrical resistances in series are added.<ref name="VR-5.2" />
[[File:fse-conduction-v2.svg|thumb|upright=1.5|alt=Three material layers with resistances adding between hot and cold surfaces.|Layer resistances add in the steady series model. Based on Van Rossum (2027), §5.2.]]

This approach makes the contribution of an insulating layer visible. A thin layer of low-conductivity material can provide substantial resistance, while a thicker layer of highly conductive material may provide less. Interface conditions and surface heat transfer still surround the conductive path.<ref name="VR-5.2" /><ref name="Atreya-1-47">Atreya (2002), p. 1-47.</ref>

Real constructions can depart from the simple layered model. In a framed wall, heat can cross through studs as well as insulation between them. Rockett and Milke demonstrate how these parallel paths change the effective heat flow. Their cavity-wall example requires a two-dimensional solution for a complete treatment.<ref name="Rockett-Milke-1-31">Rockett and Milke (2002), p. 1-31.</ref>

=== Equations and a worked example ===

For a uniform slab, the conductive heat flux equals conductivity multiplied by the temperature difference and divided by thickness. This is the steady, one-dimensional form of Fourier's law. The total heat-transfer rate is the flux multiplied by the area. Positive heat flow below is from the hotter surface to the cooler surface.<ref name="VR-5.2" /><ref name="Rockett-Milke-1-30">Rockett and Milke (2002), p. 1-30.</ref>

<math display="block">\dot q''=\frac{\lambda}{L}(T_{s,h}-T_{s,c}),\qquad \dot Q=\dot q''A</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>\dot q''</math> || Conductive heat flux || W/m²
|-
| <math>\dot Q</math> || Total heat-transfer rate || W
|-
| <math>\lambda</math> || Thermal conductivity || W/(m·K)
|-
| <math>L</math> || Layer thickness || m
|-
| <math>T_{s,h},T_{s,c}</math> || Hot and cold surface temperatures || K or °C
|-
| <math>A</math> || Area normal to heat flow || m²
|}

For several layers, their resistances add. If convection at both outer surfaces is also included, the temperature difference refers to the gases on either side. Each convective surface resistance is the reciprocal of its heat-transfer coefficient. Radiation is a separate boundary contribution and is not included by these convective resistances alone.<ref name="VR-5.2" /><ref name="Atreya-1-47" />

<math display="block">R_i=\frac{L_i}{\lambda_i},\qquad R_s=\frac{1}{h_c},\qquad \dot q''=\frac{T_{g,h}-T_{g,c}}{R_{s,h}+\sum_i R_i+R_{s,c}}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>R_i</math> || Resistance of material layer <math>i</math> per unit area || m²·K/W
|-
| <math>R_{s,h},R_{s,c}</math> || Hot and cold convective surface resistances || m²·K/W
|-
| <math>h_c</math> || Convective heat-transfer coefficient at the relevant surface || W/(m²·K)
|-
| <math>T_{g,h},T_{g,c}</math> || Hot and cold gas temperatures || K or °C
|}

Van Rossum illustrates the method with an insulated steel roof. Two steel sheets, each 0.5 mm thick, enclose 100 mm of polyurethane foam. The assumed conductivities are 45.8 W/(m·K) for steel and 0.034 W/(m·K) for the foam. Gas temperatures are 400 °C underneath and 10 °C outside, with both convective coefficients taken as 25 W/(m²·K).<ref name="VR-5.2" />

The foam resistance is approximately 2.94 m²·K/W, while each steel sheet contributes only 0.0000109 m²·K/W. Each surface resistance is 0.04 m²·K/W. Adding the five resistances and dividing the 390 K temperature difference by their total gives the following result. The calculation retains unrounded resistances until the final step.<ref name="VR-5.2" />

<math display="block">\dot q''=\frac{400-10}{0.04+0.0005/45.8+0.1/0.034+0.0005/45.8+0.04}\approx129\ \mathrm{W/m^2}</math>

This result illustrates the resistance method under fixed properties and steady conditions. It is not evidence that the foam or complete roof survives that fire exposure. Decomposition, changing properties and radiation are outside this simplified calculation. A fire-resistance assessment also requires the actual construction's thermal and mechanical behaviour over time.<ref name="VR-5.2" /><ref name="IFEG-2.6" />

== Heating over time ==

A steady state develops only after boundary conditions have remained constant long enough for the internal temperature distribution to stop changing. During the early stage, energy entering the solid changes both its stored energy and its temperature distribution. The surface can become hot while deeper material remains close to its initial temperature.<ref name="Rockett-Milke-1-29" />
[[File:fse-conduction-v3.svg|thumb|upright=1.5|alt=Temperature profiles moving deeper into a slab at early, later and steady times.|Transient conduction changes the temperature distribution through a solid. Based on Rockett and Milke (2002), p. 1-29.]]

The required initial condition includes temperature throughout the solid. Boundary conditions specify either surface temperature or heat flux at each part of its boundary over time. These inputs distinguish one conduction problem from another and cannot be replaced by a material name alone.<ref name="Rockett-Milke-1-29" />

[[Thermally thin and thick materials]] describe different responses to heat penetration. A thermally thin object can be approximated as having relatively little internal temperature variation, while a thermally thick object retains important gradients through its depth. This is a response classification that depends on heating duration, not simply geometric thickness.<ref name="VR-5.2" />

For a solid with constant properties, one-dimensional conduction and no internal heat generation, the transient equation connects temperature change with the curvature of the temperature profile. Thermal diffusivity combines conductivity with the material's ability to store energy. The equation describes how the profile evolves; it does not supply the initial or boundary conditions.<ref name="Rockett-Milke-1-29" />

<math display="block">\frac{\partial T}{\partial t}=\alpha\frac{\partial^2T}{\partial x^2},\qquad \alpha=\frac{\lambda}{\rho c}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>T</math> || Material temperature || K or °C
|-
| <math>t</math> || Time || s
|-
| <math>x</math> || Distance through the material || m
|-
| <math>\alpha</math> || Thermal diffusivity || m²/s
|-
| <math>\rho</math> || Material density || kg/m³
|-
| <math>c</math> || Specific heat capacity || J/(kg·K)
|}

Physical and chemical changes add further transient effects. Moisture can evaporate in one region, diffuse and condense elsewhere, removing and releasing energy at different locations. Decomposition and other internal changes can also act as heat sources or sinks. The simple conduction equation then needs additional terms and data.<ref name="Rockett-Milke-1-29" />

== Conduction and fire resistance ==

[[Fire resistance]] concerns the ability of a construction or member to perform required functions during fire exposure. Conduction influences the temperatures that determine separation and structural response. A barrier can remain intact against flames yet still transmit enough heat to affect its unexposed side.<ref name="IFEG-2.6" /><ref name="VR-5.2" />

For separating constructions, conductive heat flow can raise the temperature of adjacent rooms and combustible objects. For load-bearing members, the evolving internal temperature affects material properties and structural behaviour. These are different performance questions, even when both use the same heat-transfer physics.<ref name="IFEG-2.6" />

Conduction also removes energy from the fire environment. Hot gases transfer energy to walls and ceilings, and the solid then conducts part of it away or stores it. This boundary loss can influence gas temperature while simultaneously creating an exposure problem elsewhere.<ref name="VR-5.1" /><ref name="Rockett-Milke-1-29" />

An assessment should identify the quantity of interest. Heat flow through an entire area, heat flux per unit area, internal temperature and unexposed-surface temperature are not interchangeable. The required performance criterion determines which result matters and how detailed the temperature calculation must be.<ref name="VR-5.2" /><ref name="IFEG-2.6" />

== Interpreting conductive calculations ==

A conductive [[Heat transfer]] result begins with a defined temperature difference. For differences, a change of one kelvin equals a change of one degree Celsius, so either scale can express the same driving difference. Absolute temperature must nevertheless be used where another relationship, such as gas density or radiation, requires it.<ref name="VR-5.2" />

Heat flux and total heat flow answer different questions. Heat flux describes energy per unit area, while total heat flow adds the contribution over the whole exposed area. Comparing two constructions only by total watts can therefore mislead when their exposed areas differ. The relevant area and orientation must accompany the result.<ref name="VR-5.2" />

The surface temperatures used in a conduction model are not automatically equal to adjacent gas temperatures. Convection and radiation connect each gas environment to the surface, after which conduction acts within the solid. Surface resistance and solid resistance therefore belong to different parts of the wider heat-flow path.<ref name="Atreya-1-47" /><ref name="VR-5.2" />

Layer resistances provide insight into where temperature changes occur under steady conditions. A larger share of the total resistance produces a larger share of the temperature drop in the simple series model. This can help identify whether a finish, insulation layer or structural layer controls transmission, without requiring every interface temperature as an initial input.<ref name="VR-5.2" />

For wood and reinforced plastics, conductivity along the fibres may differ from conductivity across them. A layered assembly can therefore need properties for the direction of the actual heat flow. Replacing these with one average value adds an approximation to the model.<ref name="Rockett-Milke-1-28" />

== Changes within heated materials ==

Moisture changes both energy storage and transport inside porous solids. Evaporation absorbs energy at a heated location, while condensation can release energy at a cooler location after moisture diffuses through the material. The resulting heat-flow pattern is not captured by dry, constant-property conduction alone.<ref name="Rockett-Milke-1-29" />

Temperature-dependent conductivity creates a related difficulty. A value obtained near ambient conditions may not represent the same material during a severe fire. Density, specific heat and internal structure can also change, altering both the resistance and the energy needed to raise temperature.<ref name="VR-5.2" />

Char formation and decomposition introduce moving boundaries and internal heat effects. Newly formed layers can have different conductivity and thickness from the original material. Treating the original section as unchanged throughout exposure can therefore miss both insulation and consumption mechanisms.<ref name="Rockett-Milke-1-29" /><ref name="Beyler-Hirschler-1-110">Beyler and Hirschler (2002), p. 1-110.</ref>

Conductive loss to boundaries also feeds back into the fire environment. Energy entering walls and ceilings is no longer available to heat the room gas at that moment, but the stored energy can later affect surfaces and contents. Boundary conduction is thus part of the compartment energy balance, not merely an external detail.<ref name="VR-5.1" /><ref name="Rockett-Milke-1-29" />

Construction details can alter both heat flow and the barrier function. Framing creates parallel conductive paths, while cracks or holes can allow hot gases through the assembly. These mechanisms are absent from the ideal continuous-slab model. The insulation and integrity criteria of fire resistance therefore address different aspects of performance.<ref name="Rockett-Milke-1-31" /><ref name="IFEG-2.6" />

== Limits and common misunderstandings ==

Conduction is not the movement of warm material from one room to another. It is energy transfer within or between materials. Smoke crossing an opening transports mass as well as energy, whereas a wall can conduct heat without any wall material crossing to the other side.<ref name="VR-5.1" />

A low-conductivity material is not automatically a suitable fire barrier. Performance also depends on thickness, joints, thermal stability, decomposition, structural behaviour and exposure duration. Conductivity alone says nothing about whether the construction will remain intact.<ref name="Rockett-Milke-1-29" /><ref name="IFEG-2.6" />

Nor does a cool surface prove that negligible heat has entered the construction. Energy may be stored within a thick section or consumed by moisture evaporation and decomposition. The full temperature field and time history can matter more than one surface reading.<ref name="Rockett-Milke-1-29" />

Steady calculations can estimate an order of magnitude, but Van Rossum emphasises that real fires are transient. Fire power, smoke temperature and receiving-surface temperature all change. Using a steady result as a complete fire-duration prediction would exceed the model's stated purpose.<ref name="VR-5.1" />

A reliable calculation also preserves the direction of heat flow. The hot and cold surface labels must correspond to the scenario, and a negative intermediate value should not be hidden by taking an unexplained absolute number. Direction matters when assessing whether a boundary gains or loses energy.<ref name="Rockett-Milke-1-28" />

Material data need the same dimensional check as the result. Conductivity is per unit length and temperature difference, whereas heat flux is per unit area. Mixing these quantities, or entering thickness in millimetres while the property is expressed per metre, changes the answer even when the physical description is correct.<ref name="VR-5.2" />

== See also ==

* [[Biot number]]

== Notes ==

<references />

== References ==

* Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-44–1-72). National Fire Protection Association.
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing New Zealand. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Beyler, C. L., & Hirschler, M. M. (2002). Thermal decomposition of polymers. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-110–1-131). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-90–1-98). National Fire Protection Association.
* Rockett, J. A., & Milke, J. A. (2002). Conduction of heat in solids. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 1-27–1-43). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Physics & Heat Transfer]]

Reliability of fire protection systems

2026-11-01T23:17:14Z

Peter: New FSE wiki article: Reliability of fire protection systems (written by GPT-6)

'''Reliability of fire protection systems''' concerns their ability to perform the intended function under specified conditions for the required time or number of operating cycles. Modarres and Joglar-Billoch describe reliability in these terms and distinguish the physical mechanisms of failure from their probabilistic representation. In fire applications, the conditions include the demands and environmental stresses imposed by the fire.<ref name="M-24">Modarres and Joglar-Billoch (2002), pp. 5-24–5-25.</ref>

A reliability value therefore needs an explicit system boundary, success criterion and time basis. It cannot be interpreted adequately as a percentage attached to a product name. The Australian Building Codes Board (ABCB) Data Sheets require the performance level consistent with the system specification to be defined before reliability is estimated.<ref name="A-62">Australian Building Codes Board (2020a), pp. 62–64.</ref> Protection also depends on whether the functioning system is suitable, sufficiently capable and timely for the scenario. Distinguishing these questions makes reliability useful when evaluating an overall fire safety strategy.<ref name="B-194">Barry (2002), pp. 5-194–5-199.</ref>

== Function, boundaries and terminology ==

The intended function determines what counts as success. For a [[Sprinkler system|sprinkler system]], Barry describes the operational chain from water supply through pumps, valves and pipework to discharge at the heads. Whether the discharge controls the selected fire also depends on the design application. Operation and achievement of the protective objective therefore require related but distinct evidence.<ref name="B-203">Barry (2002), pp. 5-203–5-205.</ref><ref name="B-198">Barry (2002), pp. 5-198–5-199.</ref>

A [[Fire alarm system|fire alarm system]] similarly includes more than the sensing device. Barry's functional breakdown connects detection inputs, a control panel and alarms or interlocks. A reliability assessment that stops at detector operation may exclude a necessary downstream function. The boundary should extend to the output actually credited in the fire strategy.<ref name="B-205">Barry (2002), p. 5-205, Table 5-13.7.</ref>

Terminology differs between assessment frameworks. Barry separates response effectiveness, online availability and operational reliability. In this usage, response effectiveness concerns suitability, capacity, duration and response time; availability concerns whether the system is online; operational reliability concerns successful functioning on demand. These categories help identify different reasons why protection may be unsuccessful.<ref name="B-194" /><ref name="B-200">Barry (2002), pp. 5-200–5-203.</ref>

The ABCB Data Sheets use a broader definition of reliability: performance consistent with the system specification. Their examples include isolation for maintenance, common-mode failures, construction defects and doors held open. Efficacy describes achievement of the objective when the system performs to specification in the relevant scenario. The definitions must be matched before numerical values from different studies are compared.<ref name="A-58">Australian Building Codes Board (2020a), pp. 58–60.</ref>

The distinction also matters for passive measures. A barrier does not normally operate in the same sense as a pump, although doors and dampers may need to move. The ABCB framework accommodates performance distributions and defects affecting passive construction. It warns that structural reliability calculations may omit gross defects that prevent the installed protection from meeting its specification.<ref name="A-58" />

Examples of gross defects include unprotected openings, omitted protection and substitution of materials with lower performance. The ABCB Data Sheets distinguish these from ordinary variations already included in an efficacy calculation. This distinction prevents an assessment of correctly constructed protection from being treated as evidence that the installed building necessarily has that protection.<ref name="A-58" />

Success must also retain the required level of fire performance. Barry distinguishes control, suppression and extinguishment when examining capacity. A system that limits growth may meet one objective without meeting another that requires extinction. A numerical probability is meaningful only when the assessment identifies which of these outcomes constitutes successful performance.<ref name="B-198" />

== Availability, demand and duration ==

A system can be unavailable even when none of its components has failed mechanically. Planned inspection, maintenance or testing may require isolation. Repairs, false trips or operational decisions can also leave protection offline. Barry distinguishes this known or projected downtime from hidden faults that prevent operation when an apparently available system is demanded.<ref name="B-200" />

For example, a valve intentionally shut during maintenance represents unavailability in Barry's framework. A valve that is believed ready but obstructs delivery because of hidden degradation represents operational failure on demand. Both can prevent protection, but their evidence and corrective actions differ. Combining them without definitions can omit failures or count the same failure twice.<ref name="B-203" />

The mission includes continued functioning for the required duration. Successful starting does not establish that delivery, power or another necessary function will persist long enough. Modarres and Joglar-Billoch define reliability over a stated time, while Barry includes mission-time failure when examining operational performance. The required duration must follow from the protective function being credited.<ref name="M-24" /><ref name="B-204">Barry (2002), p. 5-204.</ref>

Response time is a separate constraint on useful operation. Barry evaluates protective actions against the time at which critical conditions arise at the target. A technically functioning system can respond too late for the objective. Its activation probability and its probability of responding before that deadline therefore cannot be treated as interchangeable descriptions.<ref name="B-199">Barry (2002), pp. 5-199–5-200.</ref>

Inspection and testing influence more than one part of performance. Taking equipment offline temporarily reduces availability, while the same activity may reveal hidden failures and improve subsequent operation. Barry describes this balance explicitly. An assessment should retain both effects instead of treating maintenance frequency as an automatic increase or decrease in overall reliability.<ref name="B-202">Barry (2002), p. 5-202.</ref>

False activations can also affect future availability and response. Barry describes investigations and repairs that require shutdown, extended bypasses after nuisance alarms, and occupants becoming less responsive after repeated false alarms. These mechanisms illustrate why operational history matters. A description of the installed equipment alone does not capture the conditions under which protection will be demanded.<ref name="B-202" />

== Modelling system success ==

Reliability models describe the logical requirements for success. Modarres and Joglar-Billoch explain that a reliability block diagram need not reproduce the physical arrangement of equipment. A series representation means that every represented function is required. A parallel representation means that at least one alternative can meet the complete stated requirement.<ref name="M-31">Modarres and Joglar-Billoch (2002), pp. 5-31–5-32.</ref>

For two independent functions assessed over the same mission, the simple series and parallel expressions are shown below. R<sub>1</sub> and R<sub>2</sub> are their dimensionless success probabilities. The parallel expression applies only when either function alone is sufficient. Physical duplication does not establish either independence or sufficient capacity.<ref name="M-32">Modarres and Joglar-Billoch (2002), p. 5-32, equations 37 and 42–43.</ref>

<div class="fse-equation">R<sub>series</sub> = R<sub>1</sub> × R<sub>2</sub></div>
<div class="fse-equation">R<sub>parallel</sub> = 1 − (1 − R<sub>1</sub>)(1 − R<sub>2</sub>)</div>

{| class="wikitable"
|+ Symbols in the reliability expressions.<ref name="M-32" /><ref name="H-184" />
! Symbol !! Meaning !! Unit
|-
| R<sub>1</sub>, R<sub>2</sub> || Success probability of each modelled function over the specified mission || 1, dimensionless
|-
| R<sub>series</sub> || Success probability when both independent functions are required || 1, dimensionless
|-
| R<sub>parallel</sub> || Success probability when either independent alternative alone is sufficient || 1, dimensionless
|-
| R<sub>system</sub> || Complete-system success probability, including shared requirements || 1, dimensionless
|}

The first expression requires both functions to succeed. The second calculates the probability that both alternatives fail and subtracts it from one. The probabilities must refer to compatible conditions and durations. Changing the success requirement can change the model structure even when the physical equipment remains identical.<ref name="M-31" /><ref name="M-32" />

Standby arrangements require additional attention. A reserve function may depend on detecting the need for transfer, successfully switching and then operating for the remaining mission. Modarres and Joglar-Billoch discuss these requirements separately from simple parallel operation. Treating a standby unit as an automatically successful replacement can omit the functions needed to bring it into service.<ref name="M-33">Modarres and Joglar-Billoch (2002), pp. 5-33–5-34.</ref>

[[Fault tree analysis]] provides a way to represent combinations of failures that defeat a required function, including shared support and human actions. [[Event tree analysis]] places system success or failure within the sequence following initiation. The supporting reliability model and the event-tree branch must use the same operational requirement and scenario conditions.<ref name="M-35">Modarres and Joglar-Billoch (2002), pp. 5-35–5-38.</ref><ref name="B-194" />

== Worked example with a shared supply ==

Consider a hypothetical model with two alternative delivery paths. Either path alone can meet the full requirement for the same specified mission. Given that a necessary shared supply succeeds, each path has success probability 0.95. Their remaining failures are assumed independent under that condition. These values are teaching assumptions, not measured fire-pump or sprinkler reliabilities.<ref name="M-32" /><ref name="H-184">Hall (2002), p. 1-184.</ref>

Under those assumptions, both paths fail with probability 0.05 multiplied by 0.05, or 0.0025. The probability that at least one succeeds is therefore 0.9975. This result describes the alternative paths conditional on successful shared supply. It does not yet describe the complete arrangement, because the necessary shared function has not been included.<ref name="M-32" /><ref name="H-184" />

Now assign the shared supply a hypothetical success probability of 0.98 over the required mission. The complete arrangement succeeds only when that supply succeeds and at least one delivery path succeeds. Hall's conditional-probability rule allows the shared probability to be multiplied by the conditional parallel result. The shared function is counted once.<ref name="H-184" /><ref name="M-37">Modarres and Joglar-Billoch (2002), pp. 5-36–5-38.</ref>

<div class="fse-equation">R<sub>system</sub> = 0.98 × 0.9975 = 0.97755 ≈ 0.978</div>

{| class="wikitable"
|+ Results for the hypothetical model, reported to three significant figures.<ref name="M-32" /><ref name="H-184" />
! Assessment boundary !! Success probability !! Failure probability
|-
| Alternative paths, given successful shared supply || 0.998 || 0.00250
|-
| Complete arrangement including shared supply || 0.978 || 0.0225
|}

The complete failure probability is approximately 0.0225, or 2.25%, compared with 0.250% for the alternatives when shared-supply success is certain. The difference arises from the necessary shared function. It does not mean redundancy has no benefit; it means the independent parallel calculation describes only part of the system boundary.<ref name="M-32" /><ref name="H-184" /><ref name="M-37" />

The same result can be checked by separating two mutually exclusive failure cases. Shared-supply failure contributes 0.02. When that supply succeeds, simultaneous residual failure of the two paths contributes 0.98 multiplied by 0.0025, or 0.00245. Adding these contributions gives the unrounded result 0.02245 without counting the shared failure twice. Intermediate products remain unrounded; final reported probabilities use three significant figures.<ref name="H-184" />

== Dependencies and common failures ==

[[Common cause failure]] can defeat several protective functions through one cause. Barry identifies loss of water or power, freezing, flooding and mechanical damage as relevant mechanisms. These cannot be represented adequately by assuming that every component or system fails independently. Their significance depends on which functions share the affected resource or exposure.<ref name="B-CCF">Barry (2002), pp. 5-201–5-204.</ref>

Modarres and Joglar-Billoch illustrate two suppression paths with shared water, power and actuation dependencies. Their example explicitly requires those dependencies to be included when quantifying failure. Separate pumps or nozzles do not remove a common dependency elsewhere in the chain. The analysis must follow each credited function back through its supporting functions.<ref name="M-37" />

Dependencies may also connect different types of protection. The ABCB handbook describes detection affecting occupant warning, notification of the fire service and smoke management. Their contributions cannot be evaluated solely as unrelated equipment percentages. The assessment must consider how one unsuccessful upstream function changes the conditions for each subsequent action.<ref name="A-H122">Australian Building Codes Board (2020b), pp. 120–122.</ref>

A useful model therefore identifies shared resources and common exposures before assigning independent probabilities. Where independence is not appropriate, conditional probabilities can represent the relevant relationships. Hall's definition makes clear that dependence does not require one event to cause another directly. Both may depend on a third condition that the model must retain.<ref name="H-184" /><ref name="B-CCF" />

== Data, uncertainty and continued validity ==

[[Fire statistics]] can inform reliability only when the observations match the success definition and assessed population. The ABCB Data Sheets identify historical data, fault and event trees, technical literature and expert judgement as available approaches. They also explain that evidence differs between active devices and passive construction, for which the pre-fire condition may be difficult to reconstruct.<ref name="A-62" />

Plant records can reflect the actual equipment, environment and maintenance programme, but their limitations remain important. Barry notes unrecorded failures, incomplete logs and short observation histories. Generic published data may cover different designs or operating conditions. Any adjustment requires an explicit basis rather than assuming the generic average describes the particular installation.<ref name="B-205206">Barry (2002), pp. 5-204–5-206.</ref>

Evidence at component level should not be mistaken for evidence at complete-system level. A recorded pump start does not, on its own, demonstrate that valves, distribution and discharge met the specified requirement. Barry's input, control and output breakdown identifies the interfaces that remain outside such an observation.<ref name="B-205" />

Failure rates and reliability probabilities are different quantities. A rate relates failures to time, whereas reliability concerns survival or successful performance over a specified interval. Modarres and Joglar-Billoch discuss several possible failure-time distributions. A constant-rate model is one assumption, not a universal property of fire protection equipment.<ref name="M-2529">Modarres and Joglar-Billoch (2002), pp. 5-25–5-29.</ref>

An absence of recorded failures does not establish perfect reliability. Modarres and Joglar-Billoch explain that estimates and confidence depend on the amount and quality of data and the assumed model. A short successful history leaves uncertainty about rare failures. The reported result should preserve that uncertainty rather than replace it with an unsupported value of one.<ref name="M-2529" />

The evidence basis can change during the building's life. Barry identifies age, environment, maintenance, testing, management of change and physical-damage exposure as relevant influences. The ABCB's 2020 data framework assumes appropriate installation, commissioning and continuing maintenance. Those historical assumptions need checking before its estimates are applied to an existing system.<ref name="B-207">Barry (2002), pp. 5-206–5-207.</ref><ref name="A-61">Australian Building Codes Board (2020a), pp. 61–62.</ref>

The practical consequence appears when comparing protection alternatives. The ABCB handbook presents two systems with equivalent outcomes when functioning but different failure probabilities. A deterministic assessment of successful operation alone would miss that difference. Probability information must therefore be combined with the consequences of each state before concluding that the alternatives provide equivalent protection. The same comparison must retain consequences of failure, rather than treating reliability as a complete measure of fire risk.<ref name="A-H118">Australian Building Codes Board (2020b), pp. 118–119.</ref>

A reliability assessment should retain the function, scenario, duration, boundary, dependencies, evidence and uncertainty supporting each value. These details allow later changes to be evaluated against the original assumptions. They also connect the numerical estimate to the maintenance and operational conditions needed for the credited protection to remain available and effective.<ref name="B-204" /><ref name="B-207" /><ref name="A-61" />

== See also ==
* [[Fire water supply]]
* [[Fire scenario]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020a). ''Fire safety verification method data sheets: Handbook annex'' (Version 1.1).
* Australian Building Codes Board. (2020b). ''Fire safety verification method handbook'' (Version 1.1).
* Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 5-13, pp. 5-176–5-213). National Fire Protection Association.
* Hall, J. R., Jr. (2002). Probability concepts. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 1-11, pp. 1-182–1-192). National Fire Protection Association.
* Modarres, M., & Joglar-Billoch, F. (2002). Reliability. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 5-3, pp. 5-24–5-39). National Fire Protection Association.

[[Category:Fire Risk Analysis]]

Event tree analysis

2026-11-01T23:14:12Z

Peter: Escape conditional probability bar in symbol table

'''Event tree analysis''' ('''ETA''') is an inductive method that follows an initiating event through possible subsequent events to distinct outcomes. In fire safety engineering, its branches describe how fire development, protection and human actions can alter the sequence. Barry identifies initiating events, intermediate events and outcomes as its principal elements, with the intermediate probabilities conditional on the preceding sequence.<ref name="B-180">Barry (2002), pp. 5-180–5-181.</ref>

An event tree makes the structure of a [[Fire scenario|fire scenario]] explicit. Each complete path describes one combination of events from initiation to a final state. Quantification adds probabilities or frequencies to this structure; assessing harm requires a further consequence analysis.<ref name="I-4">Australian Building Codes Board et al. (2005), p. 2.2-4.</ref><ref name="B-188">Barry (2002), pp. 5-188–5-190.</ref> The method therefore supports [[Quantitative risk assessment|quantitative risk assessment]] by connecting the likelihood of initiating conditions with the possible performance of protective measures. Its value depends on meaningful event definitions, appropriate conditional probabilities and a defensible account of the resulting consequences.<ref name="A-119">Australian Building Codes Board (2020), pp. 118–119.</ref>

== Boundaries and event sequence ==

An event tree begins with a clearly defined initiating event. This may be ignition in a particular enclosure, failure of equipment or release of a flammable substance. These starting points describe different populations of incidents. A release frequency cannot serve as a fire frequency unless the probability and circumstances of ignition are also represented.<ref name="B-181">Barry (2002), pp. 5-181–5-183.</ref>

The scope establishes what the analysis includes before branches are drawn. Barry places objectives, assessment boundaries and information gathering ahead of detailed quantification. Relevant information includes equipment, inventories, protection, operating conditions and maintenance arrangements. A tree based on the original design alone can misrepresent a facility whose equipment or operation has subsequently changed.<ref name="B-177">Barry (2002), pp. 5-177–5-179.</ref>

Intermediate events describe conditions that promote or limit the initiating event's development. Examples include detection, shutdown, isolation, automatic suppression and the performance of a barrier. An event can therefore represent a protective action or a condition that permits escalation. The headings should identify the required function rather than merely name the equipment installed.<ref name="B-180" /><ref name="B-182">Barry (2002), pp. 5-182–5-184.</ref>

The order of the headings follows the physical and operational sequence being represented. Early detection may allow isolation before a release grows, while a later intervention may act only after substantial exposure has occurred. Distinguishing these sequences prevents the same equipment from receiving identical credit regardless of when it responds.<ref name="B-182" />

A complete path ends in a defined outcome that can be assessed. The International Fire Engineering Guidelines illustrate paths involving sprinkler success, sprinkler failure followed by barrier success, and failure of both functions. These are useful structural examples. Their particular tenability outcomes depend on the assumptions of that example and cannot be assigned automatically to every protected building.<ref name="I-3">Australian Building Codes Board et al. (2005), pp. 2.2-3–2.2-4.</ref>

Fire control, suppression and extinguishment also describe different levels of performance. A successful control branch may mean that growth is limited sufficiently to meet the selected objective. It does not necessarily mean that combustion has ended. The outcome description should preserve this distinction when later assessment considers continuing heat, smoke or the duration of protection.<ref name="B-194" />

The tree is a model of the selected scenario family. Door positions, fire location, ventilation and occupant responses may require additional branches or separate initiating scenarios. The guidelines show separate fire-development and occupant-response trees, while acknowledging simplifying assumptions. Those assumptions require justification before the branches can represent an actual building.<ref name="I-56">Australian Building Codes Board et al. (2005), pp. 2.2-5–2.2-6.</ref>

== Defining success and response time ==

A branch labelled success needs a measurable functional meaning. Operation of a device and achievement of the fire safety objective are different questions. A sprinkler may operate without controlling the particular fire, while an alarm can function without producing evacuation in time. The scenario must establish which performance the branch represents.<ref name="I-3" /><ref name="A-122">Australian Building Codes Board (2020), pp. 120–122.</ref>

Barry separates response effectiveness, online availability and operational reliability when estimating protective-system success. Response effectiveness includes suitability, capacity, duration and timely action. Availability concerns whether the system is online, while operational reliability addresses its ability to perform when demanded. These distinctions support a more precise treatment of the [[Reliability of fire protection systems|reliability of fire protection systems]].<ref name="B-194">Barry (2002), pp. 5-194–5-200.</ref>

The event definition should identify a deadline where timing determines the outcome. Detection before loss of tenability differs from detection after occupants have been exposed. Similarly, isolation before a damaging release develops differs from eventual isolation. A generic probability of successful operation does not by itself establish successful operation within the required interval.<ref name="B-184">Barry (2002), p. 5-184.</ref><ref name="B-199">Barry (2002), pp. 5-199–5-200.</ref>

Timing also determines whether functions can be treated as alternatives or must occur together. The Australian Building Codes Board (ABCB) handbook illustrates evacuation as a combination of alarm, movement to safety, remaining safe and protection during exposure. Its simplified event tree is only a partial account of those interactions. More detailed analysis is needed where their relative timing affects success.<ref name="A-122" />

A branch should therefore retain the conditions under which its probability was estimated. These may include the particular fire, required output, available response time and the state of upstream systems. Replacing this description with a single percentage discards information needed to judge whether the value applies to another path or design.<ref name="B-194" /><ref name="B-190">Barry (2002), pp. 5-189–5-190.</ref>

Different levels of detail can be appropriate for different questions. A comparison involving one small change may use a simple tree, while interacting changes may require detailed supporting analysis. The ABCB handbook presents simplified probability assessment as a way to check whether differences in reliability could alter a conclusion based on deterministic modelling.<ref name="A-119" /><ref name="A-120">Australian Building Codes Board (2020), p. 120.</ref>

== Conditional probabilities and frequencies ==

Conditional probability is central to event-tree quantification. The probability assigned at a branch describes the event given the conditions already reached on that path. Hall defines the conditional probability of one event given another through their joint probability. Rearranging that definition gives the multiplication rule below, without requiring the events to be independent.<ref name="H-184">Hall (2002), p. 1-184.</ref>

<div class="fse-equation">P(A ∩ B) = P(A) × P(B | A)</div>

Here A and B are specified events, the intersection symbol denotes their joint occurrence, and the vertical bar means given. All terms are dimensionless probabilities. Applying the same rule successively gives a path probability from branch probabilities conditioned on the preceding sequence. Using unconditional probabilities instead requires an additional, justified independence assumption.<ref name="H-184" />

For a binary branch, success and failure must describe complementary outcomes under the same conditions. Their probabilities then sum to one. Across a complete set of mutually exclusive paths, the path probabilities also sum to one. These checks test the arithmetic and the stated partition of outcomes, although they cannot establish that the physical model is adequate.<ref name="H-183">Hall (2002), pp. 1-183–1-184.</ref><ref name="I-4" />

An initiating frequency adds a time basis to the calculation. Multiplying that frequency by the conditional probability of a path gives the frequency assigned to that path. This combines Barry's distinction between initiating frequencies and intermediate conditional probabilities with Hall's conditional-probability rule. The two quantities should remain separately identifiable in the results.<ref name="B-188" /><ref name="H-184" />

<div class="fse-equation">f<sub>i</sub> = f<sub>I</sub> × p<sub>i</sub></div>

Here f<sub>I</sub> is the initiating-event frequency, p<sub>i</sub> is the probability of path i given that initiation, and f<sub>i</sub> is its resulting frequency. If initiation is expressed in events per year, the path frequency has the same unit. A probability, by comparison, has no time unit.<ref name="B-188" /><ref name="H-184" />

{| class="wikitable"
|+ Symbols in the conditional-probability and frequency expressions.<ref name="H-184" /><ref name="B-188" />
! Symbol !! Meaning !! Unit
|-
| P(A) || Probability of event A || Dimensionless
|-
| P(B | A) || Probability of B conditional on A || Dimensionless
|-
| P(A ∩ B) || Probability that A and B both occur || Dimensionless
|-
| f<sub>I</sub> || Initiating-event frequency || year<sup>−1</sup> in this example
|-
| p<sub>i</sub> || Probability of path i conditional on initiation || Dimensionless
|-
| f<sub>i</sub> || Resulting frequency of path i || year<sup>−1</sup> in this example
|}

A frequency expressed per year should not be relabelled an annual probability. The former counts expected occurrences relative to time, while the latter concerns whether an event occurs within a specified interval. Keeping these meanings clear avoids mixing event frequencies, probabilities on demand and equipment failure rates in the same calculation.<ref name="B-188" />

== Worked conditional example ==

Consider a hypothetical fire initiation frequency of 0.020 per year. Automatic control succeeds with probability 0.90. If control fails, a barrier contains the fire with conditional probability 0.80. These invented values demonstrate the three-path structure illustrated in the guidelines; they do not describe measured sprinkler or barrier performance.<ref name="I-3" /><ref name="H-184" />

The first path ends with control success and has probability 0.90. The second requires control failure and subsequent barrier success, giving 0.10 multiplied by 0.80, or 0.08. The third requires failure of control and failure of the barrier under that condition, giving 0.10 multiplied by 0.20, or 0.02.<ref name="H-184" />

{| class="wikitable"
|+ Hypothetical path probabilities and frequencies, calculated using Hall's conditional-probability rule.<ref name="H-184" />
! Outcome !! Probability given initiation !! Frequency (year<sup>−1</sup>)
|-
| Automatic control succeeds || 0.90 || 0.0180
|-
| Control fails; barrier contains || 0.08 || 0.0016
|-
| Both protective functions fail || 0.02 || 0.0004
|-
| Total || 1.00 || 0.0200
|}

The barrier probability belongs only to the population of fires for which control has already failed. It is therefore conditional on that failure, including whatever fire conditions remain. The calculation does not assume that a barrier has the same chance of success during controlled and uncontrolled fires. The first path requires no additional barrier branch for this simplified outcome classification.<ref name="H-184" /><ref name="I-3" />

The path probabilities sum to one and their frequencies sum to the initiating frequency. These checks confirm that the three declared outcomes account for the assumed initiation population. The frequency 0.0004 per year describes the last path in this model. It is neither a fatality probability nor a statement that all fires outside that path are harmless.<ref name="H-183" /><ref name="A-119" />

A sensitivity case reduces conditional barrier success to 0.40 while retaining the other assumptions. The last-path probability becomes 0.10 multiplied by 0.60, or 0.06. Its frequency increases to 0.0012 per year, three times the baseline value. Automatic-control success remains unchanged, while the contained-fire path falls to 0.0008 per year.<ref name="H-184" />

This change shows how a downstream conditional assumption can affect an outcome without changing initiation or the first protective function. It does not establish which barrier value is appropriate. That requires evidence about the barrier and the exposure produced on the failed-control path, together with the functional criteria used to define containment.<ref name="B-194" /><ref name="B-190" />

== Dependencies and consequence assessment ==

Separate branches do not establish physical independence. The ABCB handbook identifies detection as an example of a function influencing evacuation, fire-service notification and automatic smoke management. Failure to detect may affect several subsequent actions together. Their probabilities must therefore reflect the detection state already reached, rather than repeatedly granting an unconditional success probability.<ref name="A-122" /><ref name="H-184" />

Occupant response can introduce another sequence alongside fire development. The guidelines distinguish occupants alerted by direct sensory cues, an alarm or other people. These routes can lead to different response times and therefore different exposure conditions. Combining occupant-response paths with fire-development paths requires attention to their shared conditions, particularly whether detection and warning have already succeeded.<ref name="I-56" /><ref name="H-184" />

[[Fault tree analysis]] can support an event-tree branch by examining the combinations of equipment, human and external failures that defeat its function. Barry describes using these methods together when simple historical estimates are inadequate. The supporting failure model must correspond to the event definition and conditions used in the event tree.<ref name="B-188" /><ref name="I-4" />

Consequences remain a separate part of the assessment. An outcome such as failed suppression identifies a system state, but does not directly quantify temperature, smoke exposure, damage or casualties. The physical and occupant-response calculations must evaluate that state. The consequence measure should correspond to the design objective against which the alternatives are being compared.<ref name="B-182" /><ref name="A-122" />

The ABCB handbook demonstrates why equal consequences conditional on operation need not mean equal risk. Two systems can provide equivalent protection when working, yet differ in how often they fail. Including their failure probabilities can change the comparison. Conversely, a high operational probability cannot compensate automatically for an inadequate result whenever the system operates.<ref name="A-119" /><ref name="B-194" />

== Evidence, uncertainty and reporting ==

Probability assignments need a traceable evidence basis. Barry identifies relevant historical experience and synthesis using fault trees, human-reliability assessment and engineering judgement as complementary approaches. Generic historical values may require adjustment for the actual facility. Differences in equipment, operating practice and management can limit their applicability to the sequence being assessed.<ref name="B-188" />

Historical incident descriptions may reveal causes and consequences without providing a usable numerical frequency estimate for the facility. Barry notes that minor events are not always reported and that records can be incomplete. The analyst must distinguish evidence that a sequence is possible from evidence of how often it occurs. The population and observation period therefore matter when interpreting a numerical assignment.<ref name="B-177" /><ref name="B-188" />

A record should preserve each event's description, probability range, source, selected value and justification. Barry's documentation example includes these fields so that assumptions remain reviewable. Where expert judgement supplies missing information, the basis and relevant expertise should be recorded. An unsupported point value remains uncertain even when subsequent arithmetic is exact.<ref name="B-190" />

[[Monte Carlo simulation]] can propagate mathematically described input uncertainty through repeated calculations. Notarianni explains that correlations between inputs need representation when generating realistic scenarios. Sampling cannot establish the correctness of an unsupported branch structure or probability distribution. The resulting spread describes the uncertainty and variability encoded in the model.<ref name="N-51">Notarianni (2002), p. 5-51 and pp. 5-54–5-55.</ref>

Reporting should connect the event tree, its probability evidence and the consequence calculations. The reader needs to identify which paths control the conclusion and which assumptions could change it. This maintains the distinction between a transparent model of possible sequences and a demonstrated judgement about the acceptability of the resulting fire risk.<ref name="B-190" /><ref name="A-119" /><ref name="N-51" />

== See also ==
* [[Fire risk assessment]]
* [[Common cause failure]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method handbook'' (Version 1.1).
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing. (2005). ''International fire engineering guidelines''.
* Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 5-13, pp. 5-176–5-213). National Fire Protection Association.
* Hall, J. R., Jr. (2002). Probability concepts. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 1-11, pp. 1-182–1-192). National Fire Protection Association.
* Notarianni, K. A. (2002). Uncertainty. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 5-4, pp. 5-40–5-64). National Fire Protection Association.

[[Category:Fire Risk Analysis]]

ETA

2026-11-01T23:13:44Z

Peter: New FSE wiki article: Event tree analysis (written by GPT-6)

#REDIRECT [[Event tree analysis]]

Event tree analysis

2026-11-01T23:13:39Z

Peter: New FSE wiki article: Event tree analysis (written by GPT-6)

Tenability criteria

2026-11-01T23:11:40Z

Peter: New FSE wiki article: Tenability criteria (written by GPT-6)

'''Tenability criteria''' are the specified conditions used to judge whether a fire environment remains compatible with an intended human activity, especially escape. They relate environmental exposure to effects such as impaired vision, painful heating, toxic incapacitation or reduced ability to move. A criterion must identify the hazard, endpoint, assessment location and relevant exposure assumptions.<ref name="purser-framework">Purser (2002), pp. 2-85–2-91.</ref>

In evacuation analysis, these criteria help establish [[Available safe egress time|available safe egress time]] (ASET). The supplied New Zealand method defines ASET as the interval from ignition to the first applicable criterion being exceeded in a specified room. Several hazards may therefore be evaluated independently before the limiting time is identified.<ref name="nz-criteria">Ministry of Business, Innovation and Employment (2025), pp. 17–18, §2.1.6.</ref>

The criteria are not universal physiological constants. Different assessment methods specify different exposure measures and assumptions. Occupant characteristics, visual targets, movement and protective equipment also matter. A result is meaningful when the numerical threshold remains connected to its intended population, scenario and design framework.<ref name="abcb-criteria">Australian Building Codes Board (2020), pp. 110–113.</ref>

== Criteria, effects and engineering decisions ==

A physiological endpoint describes a particular effect, while a design criterion specifies how an assessment uses the available evidence. Pain, impairment of escape, incapacitation and death are distinct endpoints. A model predicting one of them should not be interpreted automatically as predicting another at the same exposure.<ref name="purser-framework"/>

Purser describes a continuum of escape impairment. Smoke can reduce visibility, irritants can affect the eyes and breathing, and heat can make movement painful. These effects may slow or disrupt escape before the person reaches a nominal incapacitating dose. The analysis therefore needs to consider effective movement, rather than only the most severe outcome.<ref name="purser-framework"/>

Criteria also form part of the broader [[Acceptance criteria|acceptance criteria]] for a design. Demonstrating that one environmental quantity remains below its limit does not establish the adequacy of the complete evacuation strategy. The selected scenarios, model suitability, exposure assumptions and comparison with evacuation time also contribute to the decision.<ref name="abcb-methods">Australian Building Codes Board (2020), pp. 107–110.</ref>

The distinction between nominal response and design margin is important. Human susceptibility varies, and response models cannot reproduce every individual. Purser identifies both population variability and uncertainty in the prediction of effects as reasons for conservative interpretation when models are used for design.<ref name="purser-variability">Purser (2002), pp. 2-89–2-90.</ref>

A criterion consequently needs more than a number and unit. Its record should state the response being avoided, the population represented, the relevant time dependence and the location at which it applies. These details determine whether the model output and the criterion describe the same physical question.<ref name="purser-framework"/><ref name="abcb-criteria"/>

Occupants and firefighters illustrate the importance of population and task. The Australian Building Codes Board (ABCB) handbook discusses separate firefighter criteria based on protective clothing and breathing apparatus. It explicitly distinguishes those conditions from satisfactory design conditions for ordinary building occupants. Firefighter operating limits should therefore not be reused as occupant escape criteria.<ref name="abcb-criteria"/>

== Visibility and immediate impairment ==

[[Visibility in smoke|Visibility in smoke]] is frequently assessed because occupants need to recognise routes, obstacles and exit information. Optical attenuation reduces contrast, but the distance at which an object can be recognised also depends on illumination and the type of target. A light-emitting sign and a reflecting object need not have the same visibility.<ref name="mulholland-visibility">Mulholland (2002), pp. 2-263–2-267.</ref>

The visual task should therefore accompany the chosen criterion. A calculation for a backlit exit sign does not directly represent every object along the route. Mulholland also identifies visual acuity and adaptation to lighting as influences. Reporting a single visibility distance without these assumptions can imply greater precision than the underlying relationship supports.<ref name="mulholland-visibility"/>

Irritation adds another limitation. Some visibility correlations were derived from subjects looking through glass, which prevented direct exposure of their eyes to the smoke. An optical calculation using those correlations does not independently represent the reduction in visual performance caused by irritating gases or aerosols.<ref name="mulholland-visibility"/>

A [[Fractional effective concentration|fractional effective concentration]] approach addresses effects that depend primarily on the immediate concentration of an irritant. Purser describes a fractional irritant concentration for impairment of escape efficiency. It differs from a cumulative asphyxiant dose and can become limiting at a different time.<ref name="purser-framework"/>

These distinctions explain why a visibility criterion is an engineering choice for a specified application. It is not a universal distance below which every occupant immediately becomes incapable of escape. Familiarity, visual targets and the required task influence how an obscured environment affects movement.<ref name="purser-framework"/><ref name="mulholland-visibility"/>

Visibility can be the first limiting condition in many developing fires, but the ordering should not be assumed for every scenario. The ABCB handbook specifically calls for a supplementary carbon monoxide (CO) criterion for smouldering scenarios. Different combustion conditions and exposure histories can make another hazard controlling.<ref name="abcb-criteria"/>

== Toxic and thermal exposure ==

[[Fractional effective dose|Fractional effective dose]] (FED) accumulates an exposure relative to the dose associated with a stated effect. The calculation therefore depends on the complete relevant exposure history. A momentary concentration or temperature is not interchangeable with a cumulative dose, even when both are outputs from the same fire model.<ref name="purser-framework"/>

The contributing gases must be identified. The supplied New Zealand method states that its named CO dose assessment includes CO, carbon dioxide and oxygen. A different model may use another combination or another response expression. The label FED does not establish identical hazard coverage or identical numerical meaning.<ref name="nz-criteria"/>

The [[Effects of heat on people|effects of heat on people]] include whole-body overheating, skin pain and burns, and respiratory thermal injury. Temperature, heat flux, duration, humidity, clothing and activity affect these responses. A single air temperature cannot describe every thermal exposure mechanism or every relevant endpoint.<ref name="purser-thermal">Purser (2002), pp. 2-125–2-128.</ref>

Thermal dose models can account for both radiation and convection. The New Zealand method explicitly includes both in its thermal assessment. Their inclusion requires the relevant thermal inputs at the assessment location; a hot-gas temperature alone does not determine the incident radiation received from a nearby fire or opening.<ref name="nz-criteria"/><ref name="purser-thermal"/>

Dose and concentration criteria should remain separate unless the chosen method provides a justified combination. Adding a visibility fraction, irritant fraction and thermal dose into an unexplained total would mix different effects. Separate checks retain the ability to identify which physical mechanism limits escape first.<ref name="purser-framework"/><ref name="nz-criteria"/>

A nominal dose endpoint also differs from a guarantee of no injury. Some occupants are more susceptible, and effects can occur before the model's central endpoint. Delayed consequences can extend beyond the period of movement considered in an egress analysis. The selected criterion must therefore retain its stated purpose.<ref name="purser-variability"/><ref>Purser (2002), pp. 2-128–2-132.</ref>

== Where and when conditions are assessed ==

The assessment position determines which exposure history is being tested. A point within a [[Hot gas layer|hot gas layer]] can have different conditions from a lower position in the same room. The supplied New Zealand and ABCB methods specify evaluation at two metres above floor level for their stated occupant criteria.<ref name="nz-criteria"/><ref name="abcb-criteria"/>

That prescribed height is part of those methods. It should not be silently changed to obtain a favourable result or treated as a universal description of every occupant's breathing zone. A different population or task requires its own justified interpretation within the applicable assessment framework.<ref name="abcb-criteria"/><ref name="purser-variability"/>

The distinction between a stationary target and a moving occupant is also important. CFAST describes tenability calculations at user-specified target positions. Such an output represents conditions at the selected target. A person moving through several spaces has an exposure history that also depends on movement and time spent in each environment.<ref name="cfast-targets">Peacock et al. (2026), p. 37.</ref> Any averaging used by the model should remain explicit when assigning a local exposure.<ref name="abcb-methods"/>

An accumulated dose must be associated with the exposure period used by its model. It cannot be interpreted correctly if the record omits when exposure begins or which concentrations were encountered. Instantaneous visibility and cumulative thermal or toxic dose consequently need different treatment of the time history.<ref name="purser-framework"/><ref name="cfast-targets"/>

Fire location introduces a further spatial choice. The New Zealand method notes that several fire locations may produce the lowest ASET for a given escape route and requires consideration of multiple rooms. A result for one favourable location does not establish that the same route remains tenable for all relevant fires.<ref name="nz-criteria"/>

All time comparisons also need a common origin. The documented New Zealand definition starts ASET at ignition and compares it with the required safe egress time (RSET). An alarm-relative movement time cannot be subtracted directly from an ignition-relative ASET without accounting for the preceding detection and response period.<ref>Ministry of Business, Innovation and Employment (2025), pp. 14, 17.</ref><ref name="abcb-evacuation">Australian Building Codes Board (2020), p. 109.</ref>

== Examples of a specified criterion set ==

The supplied 2020 ABCB handbook provides a concrete example of framework-specific criteria. It identifies untenability when thermal FED exceeds 0.3 or visibility falls below the applicable distance, evaluated at the prescribed two-metre height. The visibility criterion normally uses ten metres within that framework.<ref name="abcb-criteria"/>

The same source permits five metres for rooms smaller than 100 m<sup>2</sup> or where the distance to an exit is no more than five metres. It assumes backlit exit signs unless the design brief establishes another target. These qualifications are part of the criterion and should accompany the numerical values.<ref name="abcb-criteria"/>

The handbook also requires supplementary consideration of CO for smouldering scenarios, with the criterion established through the project brief. This prevents the thermal and visibility checks from being mistaken for a complete treatment of every possible fire atmosphere. The applicable scenario determines which additional exposures need assessment.<ref name="abcb-criteria"/>

These are descriptions of the supplied edition's method, rather than universal limits or a statement of current requirements in every jurisdiction. Their engineering value is that the hazard, height, visual target and exceptions are defined together. Importing only the most favourable number would discard that context.<ref name="abcb-criteria"/>

The ABCB handbook also discusses deriving temperature-based substitutes for visibility in some comparative assessments. It notes that species production depends on the materials and combustion regime. Such a substitution therefore requires its own supported relationship; it does not mean that temperature universally predicts visibility or toxicity.<ref>Australian Building Codes Board (2020), p. 111.</ref>

The surrounding model must remain suitable for its application. The same handbook requires review of verification, validation, input relevance and the method's field of application. A well-defined criterion cannot compensate for a fire or exposure model that is unsuitable for the geometry and scenario being assessed.<ref name="abcb-methods"/>

== Worked identification of the limiting time ==

Consider an illustrative room of 150 m<sup>2</sup> with a distance to the exit greater than five metres. For this exercise, use the ABCB ten-metre visibility criterion and thermal FED criterion of 0.3 at two metres height. The following histories are invented calculation inputs, not measurements or fire-model predictions.<ref name="abcb-criteria"/>

{| class="wikitable"
! Time after ignition, s !! Illustrative visibility, m !! Illustrative thermal FED
|-
| 0 || 30 || 0.00
|-
| 60 || 24 || 0.02
|-
| 120 || 16 || 0.05
|-
| 180 || 8 || 0.17
|-
| 240 || 4 || 0.41
|}

Linear interpolation between the listed points gives a visibility threshold crossing at 165 s. The thermal dose reaches 0.3 at approximately 212 s, reported conservatively to three significant figures. Unrounded values are retained in the calculations. Under these two checks, visibility is therefore limiting. The arithmetic follows the first-criterion principle; the supplied criterion sources do not contain or validate this illustrative history.<ref name="nz-criteria"/><ref name="abcb-criteria"/>

<div class="fse-equation">t<sub>lim</sub> = min(t<sub>visibility</sub>, t<sub>thermal</sub>) = 165 s</div>

{| class="wikitable"
! Symbol !! Meaning in the example !! Unit
|-
| t<sub>visibility</sub> || Interpolated crossing time for the ten-metre criterion || s
|-
| t<sub>thermal</sub> || Interpolated crossing time for thermal FED 0.3 || s
|-
| t<sub>lim</sub> || Earlier crossing among the two evaluated criteria || s
|}

If an illustrative required egress time is 150 s from the same origin, the arithmetic difference is 15 s. That difference alone does not establish an acceptable design margin. The other applicable hazards, scenario completeness, evacuation assumptions and uncertainties have not been evaluated in this numerical exercise.<ref name="purser-framework"/><ref name="abcb-methods"/>

The interpolation is a stated numerical assumption. Actual conditions may not change linearly between stored outputs. A coarse output interval can therefore conceal a materially different crossing time. The reported precision should reflect the temporal resolution and the behaviour of the modelled quantities.<ref name="cfast-targets"/><ref name="abcb-methods"/>

The example also demonstrates why only checking the final time is insufficient. The criterion first becomes limiting before the last listed result. Identifying that first crossing preserves the relationship between evolving conditions and evacuation, rather than reducing a time-dependent assessment to one final snapshot.<ref name="nz-criteria"/>

== Uncertainty and reporting ==

Uncertainty enters through the design fire, product yields, transport, optical relationships, physiological response and evacuation behaviour. The ABCB handbook distinguishes model suitability from the selection of inputs, while Purser discusses uncertainty in human response. A numerical threshold does not remove either source of uncertainty.<ref name="abcb-methods"/><ref name="purser-variability"/>

A comparative assessment may share assumptions between a proposed design and a reference building. Shared assumptions can reduce some sensitivity, but the comparison still needs a suitable method and relevant inputs. Where a changed assumption could alter the outcome, its effect needs to remain visible in the assessment.<ref name="abcb-methods"/>

A useful result identifies the first limiting criterion, its location and time, the scenario producing it and the evacuation time used for comparison. It also states the visual target, exposure model and occupant assumptions. This allows the conclusion to be checked without reconstructing hidden choices from a final ASET number.<ref name="nz-criteria"/><ref name="abcb-criteria"/>

The resulting statement is consequently specific: the selected criteria are or are not satisfied for the assessed conditions and assumptions. It should preserve the distinction between that engineering finding and a prediction of every individual's response. That distinction keeps the tenability assessment connected to its evidence and intended use.<ref name="purser-variability"/><ref name="abcb-methods"/>

== See also ==
* [[Fire toxicity]]
* [[Optical density]]

== Notes ==
<references/>

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method: Handbook'' (Version 1.1).
* Ministry of Business, Innovation and Employment. (2025). ''C protection from fire: Verification Method C/VM2'' (2nd ed.).
* Mulholland, G. W. (2002). Smoke production and properties. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-258–2-268). National Fire Protection Association.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST: Consolidated model of fire growth and smoke transport, version 7. Volume 1: Technical reference guide'' (NIST Technical Note 1889v1, revision 7.7.7). National Institute of Standards and Technology.
* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association.

[[Category:Smoke, Toxicity & Tenability]]

Fractional effective dose (FED)

2026-11-01T23:07:08Z

Peter: New FSE wiki article: Fractional effective dose (written by GPT-6)

#REDIRECT [[Fractional effective dose]]

FED

2026-11-01T23:07:03Z

Peter: New FSE wiki article: Fractional effective dose (written by GPT-6)

#REDIRECT [[Fractional effective dose]]

Fractional effective dose

2026-11-01T23:06:58Z

Peter: New FSE wiki article: Fractional effective dose (written by GPT-6)

'''Fractional effective dose''' ('''FED''') expresses an accumulated exposure as a fraction of the dose associated with a specified effect. Fire engineering uses the concept to estimate when exposure to combustion products or heat may impair or prevent escape. The effect being modelled, the exposure-response relationship and the contributing hazards must be stated.<ref name="purser-fed">Purser (2002), pp. 2-87–2-91.</ref>

A value of one represents the nominal endpoint of the selected model. It is not a universal boundary below which every occupant remains unaffected. Human susceptibility varies, response models contain uncertainty, and design criteria can require margins relative to the nominal endpoint. FED is therefore an index for a defined assessment, not a probability of injury or survival.<ref name="purser-variation">Purser (2002), pp. 2-89–2-90.</ref>

Within [[Fire toxicity|fire toxicity]] assessment, FED links a concentration history to a physiological model. An instantaneous gas concentration alone does not describe that history. Equally, the same concentration-time product does not have an identical meaning for every gas or exposure duration.<ref name="purser-fed"/>

== Dose, endpoint and normalisation ==

The basic construction divides each increment of received dose by a reference dose associated with the selected effect. The fractions are accumulated during exposure. Where a constant reference dose is appropriate, the relationship can be written as follows.<ref name="purser-fed"/>

<div class="fse-equation">FED(t) = Σ<sub>j</sub> Δd<sub>j</sub>/d<sub>ref</sub></div>

Here Δd<sub>j</sub> is the dose received during interval j, and d<sub>ref</sub> is the effective dose for the stated endpoint. Numerator and denominator must use the same dose definition and units. Their ratio is dimensionless. The normalisation does not remove the need to explain what was measured or calculated.<ref name="purser-fed"/>

For a gas whose effect follows a constant concentration-time relationship, an increment can be represented by concentration multiplied by exposure duration. The reference dose then has matching concentration-time units. Purser describes this as a practical way to integrate a changing fire exposure until the nominal endpoint is reached.<ref name="purser-fed"/>

However, FED is more general than division by one universal concentration-time constant. Where the exposure-response relationship changes with concentration, the appropriate reference or dose-rate expression must also change. Applying an unchanged denominator to every gas would erase the physiological differences that the model is intended to represent.<ref name="purser-fed"/>

The endpoint needs equally careful definition. Purser distinguishes a fractional incapacitating dose from a fractional lethal dose. The same word dose does not make those endpoints interchangeable. A model intended to describe loss of escape capability should not be interpreted as a prediction of death at the same numerical value.<ref name="purser-fed"/>

The choice also depends on the engineering question. Impairment can delay movement before full incapacitation occurs, while some consequences develop after exposure. A calculation focused on one endpoint does not automatically address all the other ways that smoke can affect an occupant.<ref>Purser (2002), pp. 2-85–2-86, 2-90–2-91.</ref>

== Concentration-time relationships and their limits ==

[[Haber's rule|Haber's rule]] treats concentration and duration as interchangeable through a constant product for a specified effect. Under that approximation, doubling concentration halves the time required to accumulate the same dose. Purser explains both the usefulness of this concept and the circumstances in which it breaks down.<ref name="purser-fed"/>

For [[Carbon monoxide|carbon monoxide]] (CO), the physiological quantity of interest includes the accumulated carboxyhaemoglobin concentration in blood. Uptake and removal occur together. During a short exposure to a relatively high inhaled concentration, a nearly linear uptake approximation can be useful. During longer exposure at lower concentrations, equilibrium and removal become more important.<ref name="purser-co">Purser (2002), pp. 2-100–2-103.</ref>

Activity influences the calculation through respiratory minute volume and the demands placed on the person. A model for a resting subject and one for an active subject need not predict the same time to incapacitation. Body size and physiological parameters also affect the relationship between inhaled concentration and internal dose.<ref name="purser-co"/>

[[Hydrogen cyanide|Hydrogen cyanide]] (HCN) provides a contrasting example. Purser describes a strong dependence on uptake rate and concentration, with a marked departure from a constant concentration-time endpoint. A short high-concentration exposure cannot generally be treated as equivalent to a longer low-concentration exposure merely because their products are equal.<ref>Purser (2002), pp. 2-88–2-89, 2-103–2-104.</ref>

Reduced oxygen concentration introduces another response pattern. Following equilibration, the severity of oxygen-deficiency effects is strongly concentration-dependent. High carbon dioxide can also have direct effects and can increase the uptake of other gases by stimulating breathing. The mixture therefore requires more than one interchangeable dose constant.<ref name="purser-fed"/>

These distinctions matter when processing time histories. A simple average concentration may preserve a linear concentration-time product, but it need not preserve a nonlinear response calculation. The selected physiological relationship determines whether averaging, segmentation or a more complete uptake model is appropriate.<ref name="purser-fed"/><ref name="purser-co"/>

== A specified carbon monoxide dose model ==

Purser presents a short-exposure CO approximation derived from the Stewart uptake relationship. For the stated light-activity assumptions, the fraction of the nominal incapacitating dose can be calculated over discrete time intervals. The following notation keeps the exposure concentration separate from the internal endpoint.<ref name="purser-eq7">Purser (2002), p. 2-103, equation 7.</ref>

<div class="fse-equation">F<sub>CO</sub> = Σ<sub>j</sub>[a C<sub>CO,j</sub><sup>1.036</sup> Δt<sub>j</sub>/H<sub>lim</sub>]</div>

{| class="wikitable"
! Symbol !! Meaning and required convention
|-
| F<sub>CO</sub> || Dimensionless fraction of the model's CO incapacitation endpoint
|-
| C<sub>CO,j</sub> || CO concentration during interval j, entered in parts per million (ppm)
|-
| Δt<sub>j</sub> || Interval duration, entered in minutes
|-
| a || Empirical coefficient 8.2925 × 10<sup>−4</sup> for the stated units and respiratory minute volume
|-
| H<sub>lim</sub> || Nominal endpoint of 30 percent carboxyhaemoglobin, entered as 30
|}

The coefficient corresponds to a respiratory minute volume of 25 L/min and the source's light-activity condition. The denominator is expressed as a numerical percentage, rather than the fraction 0.30. Those conventions are part of the empirical equation. Changing units or percentage representation without adjusting the coefficient changes the result.<ref name="purser-eq7"/>

This is a specific historical model formulation. Its inclusion illustrates how a dose calculation is made auditable through explicit inputs and an explicit endpoint. It does not establish that this equation represents every occupant, every CO exposure pattern or the complete toxicity of a fire atmosphere.<ref name="purser-co"/><ref name="purser-variation"/>

Purser discusses the boundary between this approximation and a more complete uptake calculation. Long exposures near equilibrium, or substantial decreases in inhaled concentration, can require treatment of elimination and changing internal concentration. The simple accumulation used here does not calculate recovery following exposure.<ref name="purser-co"/>

The activity assumption affects more than the label attached to the result. Purser relates both CO uptake and the response endpoint to the subject's activity. Changing from rest to movement can therefore require reconsidering the parameter set. Retaining a fixed uptake coefficient while describing a different activity would leave an inconsistency between the exposure narrative and the numerical model.<ref name="purser-co"/>

The exponent is also part of the model. It is close to, but not exactly, one. The calculation therefore should use the stated power for each exposure segment rather than silently replacing it with a linear concentration-time expression. Numerical convenience does not justify changing the response relationship.<ref name="purser-eq7"/>

== Worked accumulation over two exposure intervals ==

Consider an illustrative CO exposure of 1000 ppm for two minutes, followed by 2000 ppm for one minute. Use the light-activity parameters above and start the calculation with zero accumulated model dose. These are selected inputs for demonstrating the calculation, not a measured fire or a permissible exposure schedule.<ref name="purser-eq7"/>

The first interval contributes approximately 0.0709 to F<sub>CO</sub>. The second contributes approximately 0.0727, giving a cumulative value of approximately 0.144 after three minutes. The calculation applies the concentration exponent separately to each interval and retains unrounded intermediate values.<ref name="purser-eq7"/>

{| class="wikitable"
! Interval !! CO, ppm !! Duration, min !! Dose increment !! Cumulative F<sub>CO</sub>
|-
| First || 1000 || 2 || 0.0709 || 0.0709
|-
| Second || 2000 || 1 || 0.0727 || 0.144
|}

The shorter second interval contributes slightly more than the first because its concentration is higher and the response is not exactly linear in concentration. This demonstrates why a cumulative dose must be calculated from the applicable response relationship, rather than inferred from duration alone.<ref name="purser-eq7"/>

Splitting either constant-concentration interval into smaller intervals gives the same accumulated result. The accompanying calculation checks one-minute, half-minute and tenth-minute subdivisions. This agreement checks the arithmetic implementation for the selected piecewise-constant history. It does not validate the physiological assumptions or establish accuracy for an unresolved changing exposure.<ref name="purser-fed"/><ref name="purser-eq7"/>

The result is only the CO component under the stated model. It excludes other gases, oxygen depletion, enhanced breathing caused by carbon dioxide, heat, obscuration and irritant effects. An overall fire assessment cannot assume those contributions are absent merely because the demonstration did not calculate them.<ref name="purser-fed"/>

Nor should 0.144 be read as a 14.4% probability of incapacitation. It is a fraction of a specified nominal endpoint. Population variability and the chosen design criterion require separate consideration. A probability model would need its own exposure-response definition and supporting parameters.<ref name="purser-variation"/><ref name="abcb-models">Australian Building Codes Board (2020), pp. 109–111.</ref>

== Mixtures, model scope and independent hazards ==

Asphyxiant assessments can combine contributions from several gases according to a defined model. Purser identifies CO, HCN and reduced oxygen as important contributors, with carbon dioxide affecting uptake. The combination rules belong to that model; they are not permission to add every available fire-hazard number without regard to its endpoint.<ref name="purser-fed"/>

Model names alone do not reveal identical coverage. The supplied CFAST reference describes a gaseous FED calculation using CO and HCN with a carbon-dioxide breathing factor. The supplied New Zealand method instead specifies that its named FED<sub>CO</sub> assessment include CO, carbon dioxide and oxygen. The contributing species must be checked explicitly.<ref name="cfast-fed">Peacock et al. (2026), p. 37.</ref><ref name="nz-fed">Ministry of Business, Innovation and Employment (2025), p. 17, §2.1.6.</ref>

Thermal dose is another application of the fractional-dose concept. Both supplied documents describe thermal assessment involving radiation and convection. Its input quantities and response equations differ from those for inhaled toxicants. A gas-dose value and a thermal-dose value should retain their separate model meanings unless a documented combination is provided.<ref name="cfast-fed"/><ref name="nz-fed"/>

[[Fractional effective concentration|Fractional effective concentration]] addresses a different type of relationship. Purser uses a fractional irritant concentration for immediate sensory effects governed by concentration. Such an index can exceed its selected endpoint even when a cumulative asphyxiant dose remains below its criterion.<ref name="purser-fed"/>

Visibility introduces another independent limitation. A low toxic dose does not establish that an occupant can see the route, identify an exit or move efficiently. The broader assessment needs the applicable optical, irritant and thermal criteria alongside the gas-dose calculation.<ref>Purser (2002), pp. 2-85–2-86, 2-130–2-132.</ref>

This separation is useful when reporting the controlling hazard. The assessment can identify whether dose, obscuration, irritation or heat first limits escape under the selected scenario. Combining unlike quantities into an unexplained total would make that physical interpretation harder to recover.<ref name="nz-fed"/><ref name="purser-fed"/>

== Endpoints, criteria and population variability ==

An FED endpoint is a model normalisation; [[Tenability criteria|tenability criteria]] state how the model is used in an engineering decision. A criterion can be set below the nominal endpoint to account for the purpose of the assessment and uncertainty. The selected value should be identified by hazard and framework.<ref name="purser-variation"/><ref name="abcb-models"/>

For example, the supplied ABCB handbook uses 0.3 for its thermal dose criterion at the prescribed assessment height. This should not be transferred automatically to a CO calculation merely because both outputs are called FED. The source treats supplementary CO assessment for smouldering scenarios separately.<ref name="abcb-models"/>

Human sensitivity is not uniform. Purser explains that underlying response models draw on limited human observations and experimental evidence, including animal studies. The nominal effect level represents a central response assumption, while susceptible groups can respond differently. That uncertainty cannot be eliminated by reporting more decimal places.<ref name="purser-variation"/>

A [[Probit function|probit function]] is one of the other human-exposure modelling approaches identified by the ABCB handbook. Its existence does not make FED itself a probability. The quantity being calculated must remain clear before a result is used to characterise the fraction of a population affected.<ref name="abcb-models"/>

The difference between toxic potency and scenario hazard is also relevant. A substance can have a high potency, but the resulting hazard depends on how much is produced and what exposure reaches the occupant. FED assessment therefore needs a scenario-specific concentration history as well as the response model.<ref name="purser-fed"/>

The history must be associated with a location or an occupant exposure path. CFAST calculates its tenability quantities at specified target positions. Such a stationary target describes conditions there; interpreting it as the complete history of a moving occupant requires additional exposure assumptions.<ref name="cfast-fed"/>

== Calculation records and interpretation ==

A reviewable FED calculation records its endpoint, contributing hazards, concentrations, time units, activity assumptions and initial condition. It identifies the exposure interval and the mathematical combination used. These details allow a reviewer to distinguish a source-term error from an exposure-history error or a response-model error.<ref name="purser-fed"/><ref name="purser-co"/>

The concentration data require their own justification. Product yields depend on the combustion conditions, and a material does not necessarily produce the same effluent in a small test and a full-scale fire. Selecting a physiological equation does not resolve uncertainty in the atmosphere supplied to that equation.<ref name="purser-fed"/>

Numerical checks should preserve the response model. Constant segments can be subdivided to check accumulation, while changing profiles require sufficient temporal detail to represent the chosen nonlinear expression. A calculation should not reset an accumulated dose at each output time or substitute a peak concentration for the full exposure history.<ref name="purser-fed"/>

The final interpretation should state the calculated dose, the criterion used and the hazards covered. It should also identify any exposure assumptions that could materially change the conclusion. This connects the mathematical fraction to the actual fire-engineering question without treating a nominal endpoint as a guarantee for every person.<ref name="purser-variation"/><ref name="abcb-models"/>

== See also ==
* [[Carbon dioxide]]
* [[Oxygen depletion]]
* [[Smoke inhalation]]

== Notes ==
<references/>

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method: Handbook'' (Version 1.1).
* Ministry of Business, Innovation and Employment. (2025). ''C protection from fire: Verification Method C/VM2'' (2nd ed.).
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST: Consolidated model of fire growth and smoke transport, version 7. Volume 1: Technical reference guide'' (NIST Technical Note 1889v1, revision 7.7.7). National Institute of Standards and Technology.
* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association.

[[Category:Smoke, Toxicity & Tenability]]

FDS

2026-11-01T23:06:25Z

Peter: New FSE wiki article: Fire Dynamics Simulator (written by GPT-6)

#REDIRECT [[Fire Dynamics Simulator]]

Fire Dynamics Simulator (FDS)

2026-11-01T23:06:20Z

Peter: New FSE wiki article: Fire Dynamics Simulator (written by GPT-6)

#REDIRECT [[Fire Dynamics Simulator]]

CFD

2026-11-01T23:06:15Z

Peter: New FSE wiki article: Computational fluid dynamics (written by GPT-6)

#REDIRECT [[Computational fluid dynamics]]

Computational fluid dynamics (CFD)

2026-11-01T23:06:10Z

Peter: New FSE wiki article: Computational fluid dynamics (written by GPT-6)

#REDIRECT [[Computational fluid dynamics]]

Sensitivity analysis

2026-11-01T23:06:04Z

Peter: New FSE wiki article: Sensitivity analysis (written by GPT-6)

'''Sensitivity analysis''' examines how calculation results change when inputs, parameters or assumptions are varied. In fire safety engineering, it helps identify which choices materially influence the predicted outcome or the resulting design decision. Notarianni distinguishes this investigation from selecting the correct value of an input: sensitivity reveals the consequences of alternatives, rather than deciding which alternative is true.<ref name="N-50">Notarianni (2002), p. 5-50.</ref> Its scope includes both measured quantities and assumptions embedded in the analysis.

Sensitivity analysis supports [[Uncertainty analysis|uncertainty analysis]] by showing where imperfect information matters. It can also identify whether a comparative conclusion remains unchanged across plausible variations.<ref name="N-51">Notarianni (2002), p. 5-51.</ref><ref name="ABCB-115">Australian Building Codes Board (2020a), p. 115.</ref> In [[Fire modelling|fire modelling]], sensitivity may concern fire inputs, occupant behaviour, model parameters or numerical choices. The selected variations and outputs must match the question being investigated, because sensitivity at one condition does not describe every possible scenario.<ref name="N-50" /><ref name="N-51" />

== What the analysis is intended to establish ==

A sensitivity study begins with an output or decision of interest. That might be a predicted temperature, a movement time or the relative performance of two designs. Changing an input is useful only when its effect is interpreted against that purpose. A large numerical change in an irrelevant output need not be important to the actual decision.<ref name="N-50" />

Notarianni describes parametric analysis as examining a sequence of values for one input while holding others constant. Plotting the resulting output shows how that parameter influences the selected criterion. The approach can reveal a trend, a threshold or a region of weak response. It does not automatically describe the consequences of several uncertain inputs changing together.<ref name="N-50" /><ref name="N-51" />

Sensitivity and uncertainty are related but distinct. An output can respond strongly to a parameter that is known accurately. Another parameter may have a weaker response but a much wider uncertain range. Assessing importance requires attention to both the response and the uncertainty assigned to the input, rather than the slope alone.<ref name="N-50" /><ref name="N-51" />

The analysis can direct further investigation towards influential information. Notarianni describes importance analysis as identifying uncertain inputs that contribute most to output uncertainty. This can help prioritise better data or a more detailed model. The result depends on the model, outcome variable and uncertainties included in the study.<ref name="N-50" />

A sensitivity study also makes hidden assumptions easier to discuss. Assumptions about route use, departure, fire growth or boundary conditions can change a design result. Making their effects explicit helps separate consequences of evidence from consequences of analyst choices. The study still cannot replace evidence about which assumptions are appropriate.<ref name="N-49">Notarianni (2002), pp. 5-49–5-50.</ref>

== Selecting inputs, ranges and comparisons ==

Input ranges need a stated basis. They may represent measurement uncertainty, plausible scenario variation or alternatives in an analysis assumption. These meanings should remain distinct because they support different conclusions. A range chosen for exploration is not automatically a probability distribution describing real-world occurrence.<ref name="N-49" /><ref name="N-51" />

Notarianni distinguishes empirical quantities from parameters expressing decisions or preferences. The latter do not necessarily have an unknown physical value that more measurement will reveal. Varying them can still show whether the design decision depends on the choice. Their treatment must make the underlying judgement visible rather than disguise it as measurement noise.<ref name="N-49" />

Bounding examines results at the extremes of an input's considered range. It can sometimes show that further detailed treatment of that uncertainty is unnecessary for the decision. That conclusion requires the examined bounds to capture the relevant response. A complex non-monotonic relationship cannot be assumed harmless merely because two endpoint calculations appear acceptable.<ref name="N-50" /><ref name="N-51" />

Changing one input at a time isolates its influence near the chosen baseline. This makes interpretation straightforward, but leaves interactions with other inputs largely unexplored. Notarianni notes that fire models can be nonlinear, multivariate and discontinuous. A single-factor study should therefore be described by its actual scope, rather than as complete coverage of uncertainty.<ref name="N-50" /><ref name="N-51" />

Correlations between inputs also require attention. Joint variations should represent combinations that are meaningful for the scenario. Treating related quantities as unrelated can produce a different uncertainty problem from the one intended. The chapter identifies correlated inputs as a feature that complicates analysis of large fire models.<ref name="N-51" />

The baseline should be documented alongside the alternatives. It gives meaning to relative changes and provides a reproducible reference. However, it is not made more credible merely by being called the baseline. The selected value and the range around it need the same scrutiny as other modelling inputs.<ref name="N-50" /><ref name="ABCB-284">Australian Building Codes Board (2020b), p. 284.</ref>

== Local measures and wider model behaviour ==

A local sensitivity describes the change in an output near a particular input state. Notarianni discusses partial derivatives as measures of response to model parameters. These can be calculated directly for some equation systems. They describe a local relationship and do not necessarily extend to a wider range where the governing response changes.<ref name="N-51" />

A numerical comparison can approximate such a derivative by perturbing an input on either side of a baseline. For an output time t and an input width W, the central difference below estimates the local slope. It is a numerical approximation to the derivative concept discussed by Notarianni. Its value depends on the chosen perturbation and the response over that interval.<ref name="N-51" />

<div class="fse-equation">S<sub>W</sub> ≈ [t(W + ΔW) − t(W − ΔW)]/(2ΔW)</div>

{| class="wikitable"
! Symbol !! Meaning in the illustrative width study !! Unit
|-
| S<sub>W</sub> || Estimated sensitivity of passage time to clear width || s/m
|-
| t || Calculated passage time || s
|-
| W || Baseline clear width || m
|-
| ΔW || Selected width perturbation on either side || m
|}

The sign identifies the direction of the local response. A negative slope means that increasing the selected width reduces the calculated time under the retained assumptions. The magnitude has units and depends on how the input and output are expressed. Raw slopes for unrelated quantities cannot be ranked meaningfully without considering units and relevant variation ranges.<ref name="N-50" /><ref name="N-51" />

Relative changes can provide another useful description. An input change can be stated as a percentage of its baseline and compared with the output's percentage change. This describes responsiveness over the selected interval. It still does not assign a probability to that interval or determine how uncertain the input actually is.<ref name="N-50" /><ref name="N-51" />

Discontinuities require particular care. A change in model state, route availability or a decision threshold can alter the form of the response. A small local derivative on one side may miss the consequence of crossing that change. The chapter therefore cautions that differential information can be useful locally without supporting a global interpretation.<ref name="N-51" />

Sensitivity can also vary with time. An input important during early fire growth may have a different influence later. The relevant output should therefore be defined as an instantaneous value, a maximum, a time to an event or another specified measure. Combining these different questions into one unexplained sensitivity number loses information needed for interpretation.<ref name="N-51" />

== Worked doorway-width study ==

Consider a deliberately simplified passage calculation for 90 people. Select a constant specific flow of 1.3 persons/(s·m) and apply the cited doorway boundary allowance of 0.15 m on each side. The baseline clear width is selected as 1.20 m. These inputs illustrate sensitivity and do not define a compliant doorway or a complete evacuation scenario.<ref name="NM-369">Nelson and Mowrer (2002), pp. 3-369–3-371.</ref>

The effective width is the clear width less the combined boundary allowance. Total flow is specific flow multiplied by effective width. Dividing the population by that flow gives the duration for the group to pass the selected point. The relationship assumes a sustained supply of occupants and the stated constant flow conditions.<ref name="NM-371">Nelson and Mowrer (2002), p. 3-371.</ref>

<div class="fse-equation">t = P/[F<sub>s</sub>(W − b)]</div>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| t || Passage duration at the selected doorway || s
|-
| P || Population passing the doorway, selected as 90 || persons
|-
| F<sub>s</sub> || Selected constant specific flow || persons/(s·m)
|-
| W || Clear doorway width || m
|-
| b || Combined boundary allowance, 0.30 m here || m
|}

At the baseline width, effective width is 0.90 m and the calculated duration is 77.0 seconds when rounded upwards to three significant figures. Reducing clear width to 1.10 m gives 0.80 m effective width and 86.6 seconds on the same rounding basis. Increasing clear width to 1.30 m gives 1.00 m effective width and 69.3 seconds on that basis. All other selected inputs remain unchanged.<ref name="NM-369" /><ref name="NM-371" />

The clear-width perturbations are approximately 8.33 percent below and above the baseline. Using unrounded durations, the resulting time changes are a 12.5 percent increase and a 10.0 percent decrease. Equal input steps therefore do not produce equal-and-opposite percentage time changes. The inverse relationship between time and effective width explains the asymmetry.<ref name="NM-371" />

Applying the central-difference expression to the unrounded alternative durations gives approximately −86.5 s/m. This is a slope estimated over the selected 0.20 m interval. It is not a universal doorway sensitivity and should not be extrapolated indiscriminately. Population, specific flow, baseline width and the boundary convention all belong to the result.<ref name="N-51" /><ref name="NM-371" />

This example concerns passage at one point. It excludes detection, response before movement, approach travel and subsequent movement. It also holds specific flow constant rather than modelling changing arrivals or congestion. Sensitivity of the simplified passage expression cannot establish sensitivity of the complete evacuation process without those additional mechanisms.<ref name="NM-367">Nelson and Mowrer (2002), pp. 3-367–3-368 and 3-372.</ref>

== Decision thresholds and changes in ranking ==

Notarianni uses the term switchover for a change large enough to alter the design decision. A prediction can vary without affecting that decision, or change only slightly while crossing an important threshold. The distinction depends on the chosen [[Acceptance criteria|acceptance criteria]]. Sensitivity should therefore connect numerical response with the criterion actually used to judge the outcome.<ref name="N-50" />

For illustration only, impose an arbitrary 80-second limit on the doorway passage example. The baseline and wider case fall below it, while the narrower case exceeds it. Solving the same expression gives a clear-width crossing near 1.17 m when rounded upwards to three significant figures. This selected threshold is an explanatory device, not an egress requirement or recommended design limit.<ref name="N-50" /><ref name="NM-371" />

The threshold example separates two sources of decision dependence. One is the response of the passage model to width. The other is the selected criterion against which that time is compared. Altering either can change the outcome, so both need clear justification in a real assessment.<ref name="N-49" /><ref name="N-50" />

In [[Performance-based design|performance-based design]], sensitivity can also concern the ranking of a proposed solution against a reference design. The 2020 handbook from the Australian Building Codes Board (ABCB) specifically discusses checking whether that ranking changes across likely input values. This asks a comparative question, rather than merely whether each prediction moves by a small percentage. Both alternatives must be assessed on a consistent basis.<ref name="ABCB-115" />

The ABCB data sheets similarly require examination of viable input variations in an evacuation-model comparison. They advise investigating unexpected responses instead of immediately assuming an error. An unexpected change may reveal an interaction or an implementation problem. Its explanation matters to the credibility of the comparative conclusion.<ref name="ABCB-284" />

== Sampling and uncertainty importance ==

[[Monte Carlo simulation|Monte Carlo simulation]] can propagate mathematically described input uncertainty through repeated model runs. Notarianni explains that the resulting outputs approximate a distribution rather than one deterministic value. Sensitivity or importance measures can then examine how inputs contribute to its variation. This requires a justified description of the uncertainty being sampled.<ref name="N-51" />

More samples can improve the numerical representation of the selected uncertainty model. They do not make an unsupported input distribution correct. Nor do they remove uncertainty from a physical mechanism omitted by the underlying fire model. Sampling quality and physical-model adequacy are separate questions.<ref name="N-50" /><ref name="N-51" />

A response surface offers another approach: outputs from selected runs are used to fit a simpler relationship. That relationship can then be explored instead of repeatedly running the full model. The usefulness depends on how well it represents the relevant behaviour. Strong nonlinearity or discontinuities can limit a simple fitted approximation.<ref name="N-51" /><ref name="N-52">Notarianni (2002), p. 5-52.</ref>

Importance rankings depend on the output, input ranges and dependence structure selected. A ranking for one scenario or time is not automatically transferable to another. It can nevertheless guide further work within the stated analysis. Improving the evidence for influential uncertain inputs may be more valuable than refining quantities with negligible decision impact.<ref name="N-50" /><ref name="N-51" />

A small sensitivity result also needs a bounded interpretation. It applies to the investigated parameter range and retained model structure. It cannot show that an omitted mechanism is unimportant, because that mechanism was never varied. Sensitivity analysis works on the represented problem and should be reported with that limit.<ref name="N-50" />

== Reporting and using the findings ==

A reproducible account identifies the baseline, varied inputs, range basis and quantities held fixed. It states the output measure and the criterion used for interpretation. The resulting changes can then be traced to the selected perturbations. Without that information, a reported percentage sensitivity has little meaning.<ref name="N-50" /><ref name="ABCB-115" />

The account should distinguish local exploration, bounding cases and probabilistic propagation. These methods answer related but different questions. A set of deterministic alternatives should not be labelled a confidence interval without an appropriate probabilistic basis. Likewise, one local derivative should not be presented as complete uncertainty in the final prediction.<ref name="N-49" /><ref name="N-51" />

The most consequential finding may be a condition that reverses the design decision. That condition should be made explicit, together with its evidential basis and whether it is plausible. Stable ranking across the examined range can also be useful evidence. Its scope remains the range, model and outputs actually examined.<ref name="N-50" /><ref name="ABCB-115" />

Sensitivity analysis ultimately supports judgement about a calculation's dependence on information and assumptions. It can identify where better data, a different representation or further scenarios would affect the conclusion. It cannot determine the correct input merely by finding a favourable result. The defensible outcome is a transparent account of what changes, why it changes and whether that matters to the decision.<ref name="N-50" /><ref name="ABCB-284" />

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020a). ''Handbook: Fire Safety Verification Method'' (Version 1.1).
* Australian Building Codes Board. (2020b). ''Data sheets: Fire Safety Verification Method'' (Version 1.1).
* Nelson, H. E., & Mowrer, F. W. (2002). Emergency movement. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-367–3-380). National Fire Protection Association.
* Notarianni, K. A. (2002). Uncertainty. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 5-40–5-64). National Fire Protection Association.

[[Category:Fire Modelling]]

Fire Dynamics Simulator

2026-11-01T23:05:59Z

Peter: New FSE wiki article: Fire Dynamics Simulator (written by GPT-6)

'''Fire Dynamics Simulator''' ('''FDS''') is a numerical model designed to simulate fire-driven flow and smoke movement. Van Rossum identifies it as a specialist application of [[Computational fluid dynamics|computational fluid dynamics]] (CFD), with Smokeview providing graphical presentation of its results.<ref name="VR-11.5">Van Rossum (2027), §11.5.</ref> The supplied technical reference describes a low-Mach-number formulation that solves transport relationships for gas flow, energy and species, with additional models for combustion, radiation and other fire processes.<ref name="F-5">McGrattan et al. (2026), pp. 5–6.</ref><ref name="F-12">McGrattan et al. (2026), p. 12.</ref>

Its default turbulent-flow treatment is [[Large eddy simulation|large eddy simulation]] (LES). Larger motions are resolved on a numerical grid, while smaller-scale effects require modelling.<ref name="F-2">McGrattan et al. (2026), pp. 2–3 and 6.</ref> This article describes the supplied sixth-edition technical reference, revision 6.11.1 dated 10 July 2026. Its assumptions and capabilities should be interpreted as those of that identified version, with application-specific evidence required before drawing engineering conclusions.<ref name="F-title">McGrattan et al. (2026), title page.</ref><ref name="VR-11.4">Van Rossum (2027), §11.4.</ref>

== Low-speed flow and the governing formulation ==

Fire-driven motion commonly involves thermal expansion, buoyancy and mixing at speeds well below the speed of sound. The FDS formulation simplifies the general fluid equations for that class of flow. The simplification allows attention to the transport processes relevant to many building fires. It does not retain every phenomenon represented by a fully compressible formulation.<ref name="F-2" /><ref name="F-10">McGrattan et al. (2026), pp. 10–11.</ref>

The guide distinguishes a background thermodynamic pressure from a smaller pressure perturbation driving motion. The background pressure enters the equation of state. The pressure and velocity solution then satisfies the expansion implied by heat release and transport. This separates the low-speed flow problem from unnecessary acoustic detail.<ref name="F-10" />

The introductory discussion associates the low-Mach approximation with velocities below Mach 0.3. It separately states that the validation discussed there extends to approximately Mach 0.1. Those are different statements about mathematical scope and supporting evidence. The broader approximation range should not be presented as demonstrated accuracy across all such flows.<ref name="F-2" />

Mass, species, momentum and energy are connected within the numerical formulation. The solver obtains mixture density from transported species densities and enforces the equation of state. Energy conservation is expressed through the velocity-divergence treatment used in advancing the flow. A successful calculation therefore depends on coupled transport, rather than independent temperature and smoke animations.<ref name="F-10" />

The default numerical method uses explicit, second-order approximations on a structured grid. The guide also lists default turbulence, combustion and radiation treatments. Optional alternatives are available for some processes, with additional computational cost. The user must justify whether the extra detail improves the prediction required for the particular application.<ref name="F-5" />

A calculation's physical meaning follows those choices. For example, using a low-speed model does not establish a capability to predict every pressure-wave phenomenon. Similarly, resolving a gas flow does not ensure that the fuel-decomposition model is appropriate. The selected scenario must remain within the demonstrated scope of the relevant equations and submodels.<ref name="F-2" /><ref name="F-12" /><ref name="VR-11.4" />

== Grid representation and resolved motion ==

FDS uses a staggered arrangement of variables. Scalar quantities such as density, temperature and pressure are associated with cell centres, while velocity components are located at cell faces. This arrangement supports the coupling of pressure and velocity. It also gives a specific numerical meaning to the locations of the calculated variables.<ref name="F-6">McGrattan et al. (2026), pp. 6–7.</ref>

[[Mesh resolution|Mesh resolution]] determines the scale at which spatial variation can be represented. In the supplied LES formulation, the filter width is associated with local cell size. Refinement changes the division between resolved motions and modelled smaller-scale effects. It therefore affects more than the visual smoothness of the output.<ref name="F-6" />

Rectilinear grids provide a convenient representation of many building features. In the basic obstruction treatment, rectangular solids align with the underlying grid. A feature smaller than the selected cells may consequently be altered or omitted in that representation. The modelled geometry must be checked against the flow paths important to the assessment.<ref name="F-6" /><ref name="VR-11.3">Van Rossum (2027), §11.3.</ref>

The supplied 2026 guide also documents a cut-cell method for more complex geometry. This qualifies the simplified rectangular-only description in Van Rossum's introductory account. The relevant capability depends on the implementation and options being used. A general statement that every FDS geometry must be reduced to rectangular obstructions would be too broad for this version.<ref name="F-6" /><ref name="VR-11.3" />

Multiple meshes can be processed in parallel. That can extend the calculation that available computing resources can support, but does not remove resolution requirements. Van Rossum recommends documenting the chosen grid, the sensitivity checks and remaining uncertainty. The purpose is to relate spatial detail to the actual prediction being relied upon.<ref name="F-6" /><ref name="VR-11.3" />

The resolved motion still represents filtered fields. A practical grid does not resolve the thin chemical reaction zones of a real flame. The guide consequently relies on submodels for mixing and combustion below the resolved scale. More cells can improve some aspects of a result without making all the underlying fire physics exact.<ref name="F-2" /><ref name="F-12" />

== Fire specification, chemistry and smoke ==

A [[Design fire|design fire]] establishes the fire scenario being assessed. Van Rossum emphasises that a CFD model does not automatically identify the real fire history for the building. Geometry, material properties and the assumed fire development must be defined during model preparation. The solver calculates the consequences of that represented scenario.<ref name="VR-11.3" /><ref name="VR-11.4" />

FDS includes models for thermal decomposition and gaseous combustion, but their use introduces further material and modelling assumptions. Their availability is different from having sufficient data to predict any furnishing or storage arrangement. The guide's introduction identifies real-material characterisation as a major difficulty. A detailed solid-phase treatment cannot replace missing evidence about the material being represented.<ref name="F-1">McGrattan et al. (2026), p. 1.</ref><ref name="F-12" />

For many applications, the combustion treatment is based on mixing-limited reaction between fuel and oxidiser. Reactants convert to products according to a characteristic mixing time. The model also provides options addressing combustion in oxygen-limited spaces. Their appropriate use depends on the conditions and level of prediction required.<ref name="F-12" />

The chemistry representation can combine several gas constituents into lumped species. For example, background air and combustion products each contain multiple primitive constituents. Transporting those mixtures reduces the number of independent equations needed for the selected reaction system. The model then recovers individual species fractions through the specified composition relationships.<ref name="F-9">McGrattan et al. (2026), pp. 9–10.</ref>

[[Soot yield|Soot yield]] is a material input with consequences for smoke and radiation. The guide's simple-chemistry treatment defines yield in relation to the mass of fuel reacted. It states that carbon monoxide and soot yields are zero by default in that treatment unless specified. A plausible smoke prediction therefore requires deliberate attention to these inputs.<ref name="F-53">McGrattan et al. (2026), p. 53.</ref>

A calculated species field must be interpreted through the reaction and transport assumptions that generated it. A correct velocity field does not independently validate a selected soot yield. Nor does an assigned yield predict how that yield changes in every ventilation condition. The model configuration and supporting fuel data remain part of the explanation of the result.<ref name="F-9" /><ref name="F-53" /><ref name="VR-11.4" />

== Radiation, surfaces and ventilation ==

The default radiation treatment solves a transport equation for a grey, absorbing gas. Absorption depends on composition and temperature, with soot playing an important role in many fires. The guide also describes optional spectral treatment. The selected representation balances computational practicality with the information available about the fire gases.<ref name="F-12" />

Radiation near flames presents a particular difficulty because grid-average temperatures can be lower than the temperatures within unresolved reacting regions. The source term therefore requires special treatment. This is a physical consequence of limited resolution, rather than merely a plotting issue. Near-fire exposure should be interpreted using the documented radiation assumptions.<ref name="F-12" />

Surface and particle processes extend the model beyond gas transport. The guide describes thermal decomposition, water and fuel droplets, and detector or sprinkler-related features. Each adds source terms or boundary conditions to the calculation. The result remains dependent on the specific model used for the represented interaction.<ref name="F-12" />

For example, the supplied water-suppression treatment includes an empirical reduction in local burning related to water present on a surface. Its coefficient depends on material and configuration. This is not a universal prediction of extinguishment for every sprinkler and fuel arrangement. The relevant empirical assumptions must be justified for the intended application.<ref name="F-103">McGrattan et al. (2026), p. 103.</ref>

Ventilation can be represented by prescribed boundary flows or by the documented heating, ventilation and air conditioning (HVAC) network solver. Fixed inlet and outlet conditions do not automatically couple the behaviour of all branches. The network representation instead links nodes and ducts through conservation equations. The distinction affects how ventilation-system interactions are represented during the fire.<ref name="F-111">McGrattan et al. (2026), p. 111.</ref>

The ventilation network can carry heat and combustion products between spaces and supply air to a fire. It can also represent parts of a smoke-control arrangement. The numerical representation must correspond to the intended operating scenario. Merely assigning an extract boundary does not establish the performance of the complete physical system.<ref name="F-111" />

== Worked grid and time-step comparison ==

Consider a selected rectangular domain measuring 20 m by 10 m by 4 m. Uniform cubic cells of 0.20 m give 100, 50 and 20 cells along the three directions. Multiplication gives 100,000 cells. Reducing the spacing to 0.10 m gives 200 by 100 by 40 cells, or 800,000 cells.<ref name="F-6" />

The refinement therefore increases the number of cells by a factor of eight. It may also require smaller time steps. The guide's Courant–Friedrichs–Lewy (CFL) constraint relates time-step size to advection across a cell. For an illustrative one-directional flow with no velocity divergence, it reduces to the expression below.<ref name="F-47">McGrattan et al. (2026), p. 47, equations 4.98–4.100.</ref>

<div class="fse-equation">CFL = UΔt/Δx</div>

{| class="wikitable"
! Symbol !! Meaning in this one-directional illustration !! SI unit
|-
| CFL || Courant number || dimensionless
|-
| U || Selected advection speed || m/s
|-
| Δt || Time-step duration || s
|-
| Δx || Cell width along the flow || m
|}

Select a velocity of 2 m/s and a Courant number of one. The illustrative time step is 0.10 seconds for 0.20 m cells and 0.05 seconds for 0.10 m cells. The finer grid therefore needs twice as many updates for the same simulated duration. These values isolate the advection relationship and are not prescribed FDS settings for a real fire.<ref name="F-47" />

For a selected 600-second duration, the corresponding counts are 6,000 and 12,000 time steps. Multiplying cell count by step count gives 600 million and 9.6 billion cell updates respectively. This simplified measure increases by a factor of sixteen. It illustrates why refining a three-dimensional transient calculation can increase work faster than the cell count alone.<ref name="F-6" /><ref name="F-47" />

This is an arithmetic comparison, not a measured runtime prediction. Actual computational work also depends on solver processes, model options and parallel execution. The full FDS stability treatment includes multiple velocity components and expansion, with other constraints where relevant. Its guide describes automatic adjustment rather than one universal fixed time step.<ref name="F-5" /><ref name="F-6" /><ref name="F-49">McGrattan et al. (2026), pp. 47–49.</ref>

The example also does not identify an acceptable mesh for a particular fire. That requires examination of the physical scales, geometry and outputs of interest. The selected 0.20 m and 0.10 m values only make the refinement arithmetic visible. Suitability must come from model documentation, sensitivity checks and relevant evidence.<ref name="VR-11.3" /><ref name="VR-11.4" />

== Outputs, visualisation and model choice ==

FDS provides a spatially varying representation of the simulated gas environment. Van Rossum describes CFD outputs such as gas temperature, velocity, smoke concentration and heat exposure. These quantities differ in meaning and evidential requirements. A useful interpretation identifies the location, time and physical quantity relevant to the engineering question.<ref name="VR-11.2">Van Rossum (2027), §11.2.</ref>

Smokeview converts simulation data into graphical representations. This can make plume development, smoke spread and changing temperatures easier to examine. It does not replace scrutiny of the underlying numerical values or assumptions. A convincing animation remains a visualisation of the selected model and inputs.<ref name="VR-11.3" /><ref name="VR-11.5" />

[[CFAST|Consolidated Fire and Smoke Transport (CFAST)]] offers a different representation based on a small number of uniform gas zones in each compartment. FDS resolves more spatial variation through its grid. The additional detail is useful when local flow and geometry matter to the assessment. It also requires suitable input information and numerical resolution to support that extra detail.<ref name="F-1" /><ref name="F-2" /><ref name="VR-9.5">Van Rossum (2027), §9.5.</ref>

The choice should therefore follow the required prediction. A compartment-average question and a local plume-deflection question do not demand the same representation. The presence of a powerful CFD tool does not itself justify every possible application. The model must represent the mechanisms governing the decision with evidence appropriate to the requested output.<ref name="F-1" /><ref name="F-2" /><ref name="VR-11.4" />

== Verification, evidence and reporting ==

The supplied technical reference documents mathematical methods, while Van Rossum emphasises comparison with suitable experimental evidence for quantitative interpretation. A model's documented capability does not eliminate uncertainty in an individual scenario. Inputs, resolution and submodel applicability must be examined together. The conclusion should remain tied to the conditions actually assessed.<ref name="F-5" /><ref name="VR-11.4" />

Grid sensitivity is one component of that examination. Results should be checked for changes that matter to the required output when resolution is altered. Time-step behaviour also deserves attention because it interacts with the resolved scales. A finer mesh with unsuitable time resolution does not automatically preserve the additional transient detail.<ref name="VR-11.3" /><ref name="F-47" />

Software identification is necessary because the available methods and defaults belong to a particular implementation. The revision used, selected physical options and important input assumptions should accompany the result. The difference between the textbook's geometry summary and the supplied technical guide demonstrates why version-specific documentation matters. Historical descriptions should not be treated as unchanging software limits.<ref name="F-title" /><ref name="F-6" /><ref name="VR-11.3" />

The final interpretation should distinguish calculated fields from the real event they approximate. Combustion, turbulence, radiation and suppression each contain assumptions that can influence the result. The output is most useful when those assumptions and the relevant evidence are visible. Numerical detail alone does not establish the accuracy of the engineering conclusion.<ref name="F-1" /><ref name="F-5" /><ref name="VR-11.4" />

== Notes ==
<references />

== References ==
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide. Volume 1: Mathematical model'' (NIST Special Publication 1018-1, 6th ed., revision 6.11.1, 10 July 2026). National Institute of Standards and Technology.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Modelling]]

Computational fluid dynamics

2026-11-01T23:05:53Z

Peter: New FSE wiki article: Computational fluid dynamics (written by GPT-6)

'''Computational fluid dynamics''' ('''CFD''') is the numerical solution of equations describing fluid motion and transport. In fire applications, it represents local conservation of mass, momentum, energy and chemical species throughout a computational domain. The domain is divided into many small cells on which the equations are approximated.<ref name="CK-194">Cox and Kumar (2002), pp. 3-194–3-196.</ref> This provides a spatially resolved form of [[Fire modelling|fire modelling]], allowing conditions to vary within rooms and around openings or obstructions.<ref name="VR-11.1">Van Rossum (2027), §§11.1–11.2.</ref>

A [[Zone model|zone model]] instead assigns representative properties to a few prescribed regions. CFD can examine variations that such a representation does not resolve, but it still requires approximations for turbulence, combustion and heat transfer.<ref name="CK-195">Cox and Kumar (2002), pp. 3-195–3-196.</ref> Its credibility depends on the physical model, numerical solution and scenario inputs. A detailed image of smoke or temperature is a presentation of those choices, rather than independent evidence of their accuracy.<ref name="CK-212">Cox and Kumar (2002), p. 3-212.</ref>

== Local conservation and the computational domain ==

The governing equations describe changes within small control volumes and exchanges across their boundaries. Flow carries mass, momentum, energy and species between neighbouring locations. Diffusion and source terms represent additional transfers or production. The calculation connects those local balances across the complete domain and advances them according to the chosen solution method.<ref name="CK-196">Cox and Kumar (2002), p. 3-196.</ref>

Mass conservation offers a useful example. Density can change with time while gas crosses the boundaries of a small region. An additional source can represent material entering the gas phase, such as evaporating droplets. The supplied Fire Dynamics Simulator (FDS) formulation expresses this balance as follows.<ref name="FDS-10">McGrattan et al. (2026), p. 10, equation 2.6.</ref>

<div class="fse-equation">∂ρ/∂t + ∇·(ρu) = ṁ<sub>b</sub>‴</div>

{| class="wikitable"
! Symbol !! Description !! SI unit
|-
| ρ || Gas-mixture density || kg/m³
|-
| t || Time || s
|-
| u || Gas velocity vector || m/s
|-
| ∇·(ρu) || Net outward mass transport per unit volume || kg/(m³·s)
|-
| ṁ<sub>b</sub>‴ || Volumetric gas mass source from represented particles or droplets || kg/(m³·s)
|}

The equation does not determine the velocity by itself. Momentum conservation relates motion to forces and stresses, while energy transport determines thermal changes. The equation of state connects density, temperature, composition and pressure according to the selected approximation. These relations are coupled, so a correct isolated balance is not a complete fire solution.<ref name="CK-196" /><ref name="FDS-11">McGrattan et al. (2026), pp. 10–11.</ref>

Chemical-species equations follow the transport and production of the represented constituents. A combustion model specifies how fuel and oxidiser produce other species and release energy. Thermal radiation and surface heat transfer contribute additional terms. Fire CFD therefore combines fluid equations with models for processes that the numerical grid cannot resolve directly.<ref name="CK-194" /><ref name="FDS-12">McGrattan et al. (2026), pp. 9–12.</ref>

The domain boundary is part of the mathematical problem. It defines where conditions are prescribed and where the model exchanges gas or heat with its surroundings. A computational boundary placed too close to an opening can influence the flow of interest. Cox and Kumar specifically caution against assuming that a fixed-pressure plane at a doorway always represents the surrounding environment adequately.<ref name="CK-boundary">Cox and Kumar (2002), pp. 3-201–3-202 and 3-206.</ref>

== Turbulence and unresolved processes ==

[[Turbulence|Turbulence]] involves motions across a range of scales. Fire plumes contain large structures as well as much smaller mixing processes. A practical building-scale calculation cannot directly resolve all the scales involved in turbulent combustion. The selected turbulence treatment determines which effects are resolved and which require approximation.<ref name="CK-195" />

Reynolds-averaged Navier–Stokes (RANS) approaches solve equations for averaged flow quantities. Additional models represent correlations associated with the unresolved fluctuations. The resulting field can describe the evolution of averages while omitting individual turbulent structures. The averaging procedure is therefore part of the physical meaning of the output, rather than merely a way of displaying it.<ref name="CK-196" />

[[Large eddy simulation|Large eddy simulation]] (LES) resolves larger turbulent motions and models effects below the effective resolution scale. It can retain more transient spatial detail than an averaged description. Nevertheless, the smaller mixing and reaction processes still require submodels. Resolving visible large eddies does not mean that the chemical reaction zone has been directly calculated.<ref name="CK-195" /><ref name="FDS-2">McGrattan et al. (2026), pp. 2–3.</ref>

In the supplied FDS formulation, the LES filter width is associated with local cell size. The represented fields can be interpreted as cell-scale averages. Changing the grid therefore affects both numerical resolution and the division between resolved and modelled turbulence. This is one reason that mesh choice cannot be separated completely from the physical modelling strategy.<ref name="FDS-6">McGrattan et al. (2026), p. 6.</ref>

Combustion and radiation introduce further approximations. The gas temperature available on a practical grid can be lower than the temperature within a thin reacting flame. Radiation treatment must account for the consequences of that limited resolution. The supplied FDS guide explicitly discusses this problem when describing its radiative source term.<ref name="FDS-12" />

The appropriate level of detail depends on the required output. A treatment adequate for overall smoke movement may be inadequate for local surface heat flux. Cox and Kumar discuss this distinction in a validation example where gas predictions and boundary heat-transfer predictions had different quality. Model credibility must therefore be assessed for the quantity being used.<ref name="CK-validationcase">Cox and Kumar (2002), pp. 3-204–3-205.</ref>

== Geometry, boundaries and the fire source ==

The geometry must represent the flow paths relevant to the problem. Openings, obstructions and the fire region influence entrainment and smoke movement. Features smaller than the represented geometry cannot be assumed to exert their real influence automatically. Simplification should therefore be judged against the mechanisms and locations important to the assessment.<ref name="CK-206">Cox and Kumar (2002), p. 3-206.</ref><ref name="VR-11.4">Van Rossum (2027), §11.4.</ref>

Grid shape and geometric capability differ between software implementations. Rectilinear representations simplify some building features, while other approaches allow different treatments of complex surfaces. The relevant limitation is the one documented for the chosen implementation and version. A restriction associated with one grid treatment should not be presented as a universal restriction on CFD.<ref name="VR-11.3">Van Rossum (2027), §11.3.</ref><ref name="FDS-6" />

The fire source requires a justified physical description. Heat release, fuel properties and the area or volume over which the source is imposed influence buoyant motion. Cox and Kumar show that a poorly chosen source size can produce implausible temperatures and distort entrainment. A visually plausible plume is therefore insufficient evidence that the source specification is appropriate.<ref name="CK-206" />

The building surfaces also affect the result. Heat transfer depends on thermal properties and changing surface temperatures, not simply on the existence of a wall. The gas calculation and conduction into the solid must use compatible boundary conditions. An approximation adequate for smoke movement may need refinement when surface heating becomes the principal output.<ref name="CK-boundary" />

Ventilation inputs must describe the intended physical system. Prescribed inlet or outlet conditions can be useful, but do not necessarily reproduce interactions between several branches of a heating, ventilation and air conditioning (HVAC) network. The supplied FDS guide distinguishes such fixed boundaries from a coupled duct-network solver. The assessment must identify which representation is being used and what it assumes.<ref name="FDS-HVAC">McGrattan et al. (2026), p. 111.</ref>

Initial conditions matter when a calculation follows fire development in time. The model starts from a selected thermal and flow state before subsequent changes are applied. Van Rossum places these scenario and material choices within model preparation. The solver then calculates the consequences of that defined problem, rather than selecting an undocumented real fire history.<ref name="VR-11.3" /><ref name="VR-11.4" />

== Mesh, time resolution and numerical error ==

[[Mesh resolution|Mesh resolution]] controls how finely the domain and its changing fields are represented. More cells can describe smaller geometrical and flow features. They also increase computational demand. Van Rossum emphasises that finer cells do not automatically make an entire result more trustworthy, because the other inputs and submodels remain relevant.<ref name="VR-11.3" />

Discretisation replaces continuous derivatives with finite numerical approximations. Cox and Kumar explain how omitted terms create truncation error. Some approximations can act like additional diffusion and smooth the calculated field. A smooth contour can consequently reflect numerical behaviour as well as the physical mixing represented by the model.<ref name="CK-202">Cox and Kumar (2002), pp. 3-202–3-203.</ref>

Refinement studies examine whether the outputs of interest change materially as the grid is altered. They must focus on the locations and quantities relevant to the assessment. Agreement at one monitoring point does not establish that all parts of the solution have comparable resolution. The fire region, openings and vertical buoyant flow deserve particular attention in the cited guidance.<ref name="CK-206" /><ref name="VR-11.3" />

Time resolution is a separate but connected issue. A transient calculation must use time steps appropriate to its grid and numerical scheme. Excessively large steps can lose temporal detail or violate stability conditions. The FDS guide relates advection time stepping to how far fluid can travel across a cell during one update.<ref name="CK-206" /><ref name="FDS-47">McGrattan et al. (2026), pp. 47–49.</ref>

Numerical convergence has several meanings that should remain distinct. An iterative solution can satisfy its discrete equations closely while still changing when the grid is refined. Conversely, a small change between iterations can result from strong underrelaxation rather than an adequately converged solution. Cox and Kumar warn against relying on slowly changing residuals alone.<ref name="CK-202" />

Those iterative observations arise from the RANS solution methods discussed in the handbook chapter. They should not be imposed unchanged on every transient LES algorithm. The applicable checks depend on the solver's documented method. The broader requirement is to demonstrate adequate solution accuracy and stability for the numerical formulation actually used.<ref name="CK-202" /><ref name="FDS-6" /><ref name="FDS-47" />

== Worked conservation check across two cells ==

Consider two illustrative adjacent gas cells, each initially containing 1.20 kg. Select an external inflow of 0.30 kg/s into the first cell. Let 0.25 kg/s pass from the first cell to the second, while 0.20 kg/s leaves the second cell externally. Assume these rates remain fixed for 10 seconds, with no additional gas mass source.<ref name="CK-196" /><ref name="FDS-10" />

The first cell accumulates 0.05 kg/s, because its inflow exceeds transfer to the second cell by that amount. It therefore gains 0.50 kg and finishes with 1.70 kg. The second cell also accumulates 0.05 kg/s, giving the same final mass. These results follow from the selected flow accounting.<ref name="FDS-10" />

Across both cells together, the internal transfer cancels. It is an outflow from one cell and an equal inflow to the other. The external net input is 0.10 kg/s, so total mass rises from 2.40 kg to 3.40 kg over the interval. Summing the individual cell balances gives the same result.<ref name="CK-196" /><ref name="FDS-10" />

This example illustrates a necessary conservation check. If the shared face used inconsistent transfers on its two sides, the combined balance would contain an artificial source or sink. Consistent local accounting is therefore connected to global conservation. The overall balance provides one way to examine the assembled numerical result.<ref name="CK-203">Cox and Kumar (2002), p. 3-203.</ref>

The prescribed rates are not predictions of a complete CFD solver. A physical solution would also require momentum, energy and state relationships to determine compatible flows and thermodynamic conditions. Passing this arithmetic check cannot establish the accuracy of those other processes. It demonstrates why conservation is necessary while remaining insufficient for validation.<ref name="CK-196" /><ref name="CK-203" />

== Verification, validation and application evidence ==

[[Verification and validation|Verification and validation]] address different questions. Verification concerns whether the implementation and numerical solution accurately represent the intended model. Validation concerns how well that model represents the real system for its intended use. A calculation can solve its chosen equations accurately while those equations or submodels remain unsuitable for the application.<ref name="CK-203" />

General fluid-flow benchmarks provide useful evidence about a solver, but do not cover every fire-specific mechanism. Buoyancy, combustion and radiation introduce additional questions. Cox and Kumar specifically distinguish general CFD capability from validity for fire applications. Relevant evidence must address the processes governing the actual prediction.<ref name="CK-203" />

Experimental comparisons should also match the output being used. Gas temperature, species concentration and heat flux are different quantities with different measurement and modelling difficulties. The handbook's discussion of boundary heat transfer illustrates this point. Agreement in one output cannot be transferred automatically to another without examining the responsible submodels.<ref name="CK-validationcase" />

Global mass and energy balances remain valuable diagnostic checks. They can reveal inconsistency even when local images appear plausible. However, a satisfactory global balance can coexist with an inaccurate distribution inside the domain. The cited chapter therefore combines balance checks with convergence, refinement and physical scrutiny of the important flow regions.<ref name="CK-203" /><ref name="CK-206" />

[[Fire Dynamics Simulator|Fire Dynamics Simulator]] is one fire-focused CFD implementation discussed by Van Rossum. Its technical reference documents a particular combination of equations and submodels. Evidence for that combination does not automatically validate a different program, different model options or another version. Software identification belongs alongside the scenario and numerical settings in the assessment.<ref name="VR-11.5">Van Rossum (2027), §11.5.</ref><ref name="FDS-5">McGrattan et al. (2026), pp. 5–6.</ref>

== Interpreting and presenting the result ==

Preprocessing defines geometry, materials, scenarios and inputs; the solver performs the numerical calculation; postprocessing turns its results into plots and other displays. These functions serve different purposes. A postprocessor can reveal patterns that deserve investigation, but cannot independently verify the assumptions that produced them. The underlying numerical quantities remain the evidence being interpreted.<ref name="VR-11.3" />

The reported conclusion should identify the quantities, locations and times actually assessed. It should explain why the chosen resolution and physical treatment are appropriate. Important input assumptions and remaining uncertainties must remain visible. This allows a reader to judge the conclusion against the model's demonstrated capabilities.<ref name="VR-11.3" /><ref name="VR-11.4" />

CFD is particularly useful when the question depends on spatial variation that a simpler representation cannot adequately describe. Its detail nevertheless carries responsibilities for geometry, boundaries, submodels and numerical checks. The final result is a conditional prediction of a defined scenario. Interpretation must retain those conditions instead of treating the visualisation as the event itself.<ref name="CK-195" /><ref name="CK-212" /><ref name="VR-11.4" />

== See also ==
* [[Fire investigation]]
* [[Soot yield]]
* [[Adiabatic surface temperature]]

== Notes ==
<references />

== References ==
* Cox, G., & Kumar, S. (2002). Modeling enclosure fires using CFD. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-194–3-218). National Fire Protection Association.
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide. Volume 1: Mathematical model'' (NIST Special Publication 1018-1, 6th ed., revision 6.11.1, 10 July 2026). National Institute of Standards and Technology.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Modelling]]

Individual risk

2026-11-01T23:03:31Z

Peter: Add source-supported link to Probit function from ABCB Handbook p. 110

'''Individual risk''' expresses the likelihood of a specified injury or death affecting an individual at a defined location or under defined exposure conditions. Barry describes it relative to a fire or explosion source. His location-based contours show the expected frequency of events capable of causing the specified harm, regardless of whether anyone actually occupies the location.<ref name="B210">Barry (2002), p. 5-210.</ref>

The quantity therefore needs an explicit meaning before it can support a decision. A geographical measure for a continuously exposed hypothetical person differs from the risk experienced by somebody whose presence and protective actions vary. The ABCB Handbook also distinguishes individual risk from the likelihood of multiple deaths within a building. These measures answer related but different questions.<ref name="B210" /><ref name="A22">Australian Building Codes Board (2020), p. 22.</ref>

An assessment combines the frequency of relevant scenarios with their potential consequences. Its numerical result remains conditional on the selected harm endpoint, exposure assumptions and evidence. Presenting the result as a contour, profile or single value does not remove those conditions.<ref name="B176">Barry (2002), p. 5-176.</ref><ref name="B211">Barry (2002), p. 5-211.</ref>

== Defining the person, location and harm ==

The definition of harm sets the question being answered. A calculation concerned with fatality cannot be relabelled as a calculation of any injury. Barry notes uncertainties in fatal thermal, blast and toxic exposures. Assumptions and judgements about these endpoints require documentation, including when the assessment extends from fatalities to injuries.<ref name="B211" />

The exposure description is equally important. A location-based measure can describe the potential for harm at a fixed position without estimating the actual number of people present. This is useful for displaying a geographical pattern. It should not be interpreted as a population casualty estimate merely because the contour crosses an occupied area.<ref name="B210" />

An actual-person interpretation requires assumptions about the circumstances of exposure. Barry identifies population presence and the reliability of mitigation, including evacuation, when extending an assessment to people around a facility. These assumptions distinguish potential exposure from realised consequences. Their treatment needs to remain consistent between the scenario calculations and the reported risk measure.<ref name="B211" />

Within [[Fire risk|fire risk]] assessment, individual risk is therefore a defined output rather than a complete description of safety. It can identify locations or scenarios needing attention, but it does not describe every consequence of a fire. Property damage, interruption and the number of people affected may require other outputs alongside the individual measure.<ref name="B176" /><ref name="B210" />

The ABCB Handbook lists simple tenability limits, fractional effective dose models and [[Probit function|probit functions]] as forms of human exposure model. These categories describe alternative representations of human response. Their endpoint and interpretation need to be identified before using the outputs in an individual-risk calculation.<ref name="A110">Australian Building Codes Board (2020), p. 110.</ref><ref name="B211" />

== Combining scenario frequencies and conditional harm ==

The basic calculation connects how often a scenario occurs with what follows when it occurs. Barry expresses risk as event frequency multiplied by expected consequence and describes summing contributions from selected scenarios. For individual harm, a conditional probability can represent the consequence term, provided its endpoint and exposure assumptions are specified.<ref name="B176" /><ref name="B208">Barry (2002), pp. 5-208–5-209.</ref>

The following expression is a specialisation of that frequency–consequence approach. It represents the expected annual frequency of the selected harm at a location. The scenarios must be distinct contributions to the model, so that an initiating event and its own outcome branches are not counted twice.<ref name="B208" />

<div class="fse-equation">R(x) = Σ<sub>i</sub> f<sub>i</sub> p<sub>i</sub>(x)</div>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| R(x) || Expected frequency of the selected harm at location x || year<sup>−1</sup>
|-
| f<sub>i</sub> || Frequency of distinct scenario i || year<sup>−1</sup>
|-
| p<sub>i</sub>(x) || Conditional probability of the selected harm at x, given scenario i and the stated exposure assumptions || dimensionless
|-
| x || Defined location || location identifier or spatial coordinates
|}

Frequency and probability have different units. In this expression, a frequency per year multiplied by a dimensionless conditional probability produces a frequency per year. Calling that result an exact annual probability would introduce a further interpretation that the expression itself does not establish. The report should retain the quantity and units actually calculated.<ref name="B176" /><ref name="B210" />

The scenario frequencies already need to incorporate the relevant sequence of events. If a frequency includes failed suppression, that failure should not be applied again within the same contribution without a clear reason. Barry's scenario approach connects initiating conditions, protection performance and outcomes before combining their risk contributions.<ref name="B208" />

[[Quantitative risk assessment|Quantitative risk assessment]] supplies this broader structure. A single exposure calculation gives information about a consequence under selected conditions. It does not establish how often those conditions arise. Conversely, an initiating-event frequency cannot determine individual harm until the subsequent scenario and exposure have been represented.<ref name="B176" /><ref name="B208" />

== A numerical illustration ==

Consider three distinct hypothetical scenarios affecting one selected location. Assume a person is present there for the exposure represented in every case. The frequencies and conditional probabilities below are chosen solely to demonstrate arithmetic. They are neither incident data nor recommended design values.<ref name="B208" />

{| class="wikitable"
! Scenario !! Frequency (year<sup>−1</sup>) !! Conditional probability of harm !! Contribution (year<sup>−1</sup>)
|-
| A || 0.001 || 0.10 || 0.000100
|-
| B || 0.0002 || 0.50 || 0.000100
|-
| C || 0.00005 || 0.90 || 0.000045
|-
| Total || Not applicable || Not applicable || 0.000245
|}

Scenario A occurs five times as frequently as B, but its conditional probability of harm is one fifth as large. Their contributions are consequently equal. Scenario C has the highest conditional harm probability but the smallest contribution because its assumed frequency is lower. Ranking consequences alone would therefore give a different order from ranking these risk contributions.<ref name="B176" /><ref name="B208" />

The first two scenarios each contribute approximately 40.8% of the total; C contributes approximately 18.4%. These proportions can help identify which assumptions drive the result. They do not show which intervention is feasible, reliable or proportionate. Barry treats selecting risk-reduction measures as a subsequent analysis of the available options.<ref name="B211" />

For a second arithmetic case, reduce only B's conditional probability from 0.50 to 0.10. Its contribution becomes 0.000020 per year, and the total becomes 0.000165 per year. This illustrates consequence reduction with unchanged initiating frequencies. It does not demonstrate that a particular protection system can deliver the assumed change.<ref name="B176" /><ref name="B211" />

Neither total establishes acceptability. No acceptance threshold, justified scenario frequencies or validated harm relationships have been supplied in this illustration. The example shows how inputs combine and how one selected change affects the output. A building or facility conclusion requires evidence for those inputs and an independently defined decision criterion.<ref name="B208" /><ref name="A44">Australian Building Codes Board (2020), p. 44.</ref>

== Profiles, contours and population measures ==

A risk profile plots a selected measure against distance or another specified spatial path. A contour connects locations having the same potential individual risk. Barry describes both presentations as ways to communicate the geographical distribution of fire and explosion risk. The harm endpoint and exposure convention must accompany either display.<ref name="B210" />

Contour geometry depends on the scenario analysis. The source presents an industrial layout with different activities and surrounding land uses, rather than a universal circular boundary. A schematic contour therefore cannot substitute for calculated exposure fields. Likewise, a profile along one direction does not describe every other direction around a facility.<ref name="B210" />

[[Societal risk|Societal risk]] additionally considers multiple casualties. Barry describes cumulative frequency–fatality curves and the information needed about the exposed population, its presence and mitigation. An individual-risk contour alone does not contain that population information. Two assessments can consequently have similar individual measures while involving different numbers of exposed people.<ref name="B210" /><ref name="B211" />

The ABCB Handbook calls for individual and societal risk to be considered together in its comparative building strategy. This makes the distinction relevant even when the assessment compares two designs rather than mapping an industrial site. A design change affecting occupancy can alter the population consequence without an equivalent change in the potential harm at one location.<ref name="A22" />

== Evidence, uncertainty and comparison ==

Scenario frequency estimates can draw on plant records, generic information and expert judgement. Barry discusses their quality alongside maintenance, testing and common-cause effects. A numerical estimate should therefore retain its origin and applicability. A rate drawn from another operating context is not automatically a measured rate for the installation being assessed.<ref name="B206">Barry (2002), pp. 5-206–5-207.</ref>

Uncertainty also enters the consequence calculation and the conversion from exposure to harm. Barry recommends documenting the judgements behind human-risk endpoints and discusses uncertainty bands when presenting results. Reporting many decimal places cannot compensate for uncertain inputs. The useful precision of the result depends on the evidence supporting the calculation.<ref name="B208" /><ref name="B211" />

The purpose of the comparison determines which output is useful. Barry distinguishes comparisons of design, operational and protection options and warns against presentation that hides resolution or introduces bias. The same endpoint, exposure convention and scenario basis are needed to interpret differences between alternatives. A changed definition can otherwise appear as a changed risk.<ref name="B211" />

The ABCB Handbook illustrates a reference-building approach for deriving comparative individual and societal risk criteria. That historical framework does not provide a universal numerical limit for every building or industrial installation. The selected reference and departures need to be documented so the calculated difference can be related to the assessment's objectives.<ref name="A44" />

Risk reduction can address scenario frequency, consequence severity or both. Barry identifies equipment reliability, ignition prevention, detection and protection among the available approaches. The resulting individual-risk estimate remains conditional on their assumed performance. A useful report therefore connects the numerical result with the specific conditions and measures needed to maintain it.<ref name="B211" />

== See also ==
* [[Acceptance criteria]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method handbook'' (Version 1.1).
* Barry, T. F. (2002). Quantitative risk assessment in chemical process industries. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 5-176–5-213). National Fire Protection Association.

[[Category:Fire Risk Analysis]]

Effects of heat on people

2026-11-01T23:03:17Z

Peter: New FSE wiki article: Effects of heat on people (written by GPT-6)

'''Effects of heat on people''' are the physiological and behavioural consequences of thermal exposure during a fire. Fire engineering distinguishes impaired escape, incapacitation and injury because they are different outcomes. Heat can obstruct evacuation through pain before a person becomes physically incapable of movement or suffers the most severe consequences of exposure.<ref name="purser-escape">Purser (2002), pp. 2-85–2-86.</ref>

The principal thermal mechanisms are whole-body overheating, burns to the body surface and thermal injury to the respiratory tract. Their development depends on both the exposure and the person. Duration, incident heat, humidity, air movement, clothing and activity influence the response; air temperature alone does not describe every relevant condition.<ref name="purser-heat">Purser (2002), pp. 2-125–2-128.</ref>

Engineering assessments translate these effects into [[Tenability criteria|tenability criteria]] suited to a particular scenario and occupant population. A criterion based on pain, a cumulative thermal dose and a criterion for severe injury answer different questions. The endpoint and the conditions behind the chosen model must therefore accompany any numerical limit or predicted exposure time.<ref name="abcb-human">Australian Building Codes Board (2020), pp. 109–111.</ref>

== Heat transfer and the exposed person ==

A thermal exposure describes the transfer of energy to the person, rather than merely the temperature of the surroundings. The relevant [[Heat flux|heat flux]] expresses the rate of energy transfer per unit area. The resulting tissue heating depends on how that energy is absorbed, distributed and removed during the exposure.<ref name="purser-skin">Purser (2002), pp. 2-126–2-127.</ref>

Radiation, convection and conduction provide distinct transfer paths. Radiation can heat exposed skin from a flame, hot surface or hot gas region without direct contact. Convection transfers heat between moving gases and the body. Conduction becomes important when skin contacts a hot object.<ref name="purser-skin"/>

These paths need different environmental information. A gas temperature does not specify the radiation received from a nearby opening. Equally, a radiant flux does not define the convective heating caused by surrounding hot gases. A calculation should identify which mechanisms are represented and which exposure quantities its response model requires.<ref name="purser-heat"/>

Convection depends on air movement and humidity as well as temperature. The same nominal air temperature can therefore produce different heating under different flow conditions. For contact heating, the material properties of the object influence the interface temperature and heat transfer. A metal surface and a low-conductivity surface need not produce the same contact exposure.<ref name="purser-skin"/>

The body is also not a uniform passive target. Different regions may be covered or exposed, and activity changes heat production and the demands of movement. Purser identifies the amount and type of clothing and the work being performed as significant influences on thermal tolerance.<ref name="purser-heat"/>

A useful engineering exposure description consequently states the location, duration, principal transfer mechanisms and assumed protection. This creates a traceable connection between the fire calculation and the response model. A single reported temperature or flux is insufficient when the omitted conditions materially affect the chosen endpoint.<ref name="purser-heat"/><ref name="abcb-human"/>

== Hyperthermia, skin pain and burns ==

Hyperthermia results when the body accumulates heat faster than it can remove it. It can develop during prolonged exposure at conditions that do not immediately burn the skin. Activity and impaired evaporative cooling can increase the burden. It is therefore a different mechanism from the rapid surface heating associated with intense radiation.<ref name="purser-heat"/>

Skin pain and burns depend on the thermal history of the exposed tissue. The balance between incoming heat and heat conducted away controls the temperature rise near the surface. Duration matters because the tissue continues to accumulate heat while exposure persists. A brief intense exposure and a longer moderate exposure cannot be compared by peak temperature alone.<ref name="purser-skin"/>

Pain, partial-thickness injury and more extensive burns are separate endpoints. A relationship developed for the onset of pain should not be relabelled as a relationship for fatal injury. Conversely, an analysis that only predicts severe injury can miss an earlier condition that prevents occupants from continuing along a route.<ref name="purser-escape"/><ref name="purser-skin"/>

Purser describes a continuum of impairment. Discomfort and pain can reduce the efficiency of escape before a sharply defined incapacitating event occurs. Some effects, such as loss of consciousness from other fire hazards, have a clearer endpoint than the point at which painful conditions stop effective movement.<ref name="purser-escape"/>

Clothing has a conditional role. It can reduce immediate heat transfer to covered skin, while leaving the head or other regions exposed. During longer exposures, clothing can also restrict evaporative heat loss. Treating clothing as a single constant increase in tolerance would conceal these different effects.<ref name="purser-heat"/>

These distinctions explain why a temperature limit requires context. The same number may be used as a screening criterion in one method and as an input to a time-dependent response model in another. Its meaning depends on the exposure duration, humidity, body region and endpoint for which it was selected.<ref name="purser-heat"/><ref name="abcb-human"/>

== Humidity and respiratory thermal exposure ==

Humidity affects both the removal of body heat and the delivery of heat to tissue. Moist air can restrict cooling by evaporation. Steam can also transfer substantial energy when it condenses. A dry-air exposure relationship therefore cannot automatically be transferred to an atmosphere containing a large amount of water vapour.<ref name="purser-humidity">Purser (2002), pp. 2-127–2-128.</ref>

The distinction is especially important for the respiratory tract. Purser describes the limited thermal capacity of dry air and the cooling effect of the moist airway surfaces. Steam and other atmospheres with greater thermal capacity can produce a different pattern of thermal injury. Temperature alone does not capture that difference.<ref name="purser-humidity"/>

Fire atmospheres complicate interpretation because several mechanisms may act together. Inhaled irritants can cause chemical injury, hot gases can transfer heat, and body-surface burns can have subsequent systemic consequences. Observed respiratory damage cannot always be assigned to thermal inhalation alone.<ref name="purser-humidity"/>

This is a limitation on the engineering inference, rather than a reason to omit respiratory effects. A model using gas temperature as a thermal indicator should state whether humidity and other properties of the atmosphere are represented. Separate toxic effects remain relevant even when a thermal criterion is satisfied.<ref name="purser-humidity"/><ref name="purser-escape"/>

The source material also distinguishes immediate escape impairment from effects that develop after exposure. A person leaving the hazardous environment has not necessarily avoided every injury endpoint. Egress calculations address a defined period and outcome; they should not be interpreted as a complete clinical prognosis.<ref>Purser (2002), pp. 2-85–2-86, 2-128.</ref>

The practical consequence is to preserve the model's stated exposure conditions. A criterion derived for dry air, exposed skin or resting subjects represents those assumptions. Changing the humidity, protective clothing or physical activity changes the physical problem, even if the reported gas temperature is unchanged.<ref name="purser-heat"/>

== Thermal criteria and cumulative exposure models ==

The ABCB handbook distinguishes simple exposure limits from more detailed human-response models. It identifies fractional effective dose and [[Probit function|probit functions]] among the available approaches, while noting that simple limits and dose models are commonly used for building fire assessments. These are different ways of representing an exposure-response relationship.<ref name="abcb-human"/>

A simple limit compares a selected environmental quantity with a prescribed threshold. A dose model considers the accumulated effect of exposure over time. The distinction matters when conditions change during evacuation: an instantaneous value does not contain the same information as the complete exposure history.<ref>Purser (2002), pp. 2-128–2-131.</ref>

A thermal fractional effective dose can accumulate contributions from radiant and convective exposure according to the selected model. The supplied New Zealand verification method explicitly requires both contributions for its thermal assessment. Their inclusion does not mean that every published thermal equation uses the same coefficients, assumptions or endpoint.<ref name="nz-tenability">Ministry of Business, Innovation and Employment (2025), p. 17, §2.1.6.</ref>

The choice of criterion also belongs to a stated design framework. The supplied 2020 ABCB handbook uses a thermal dose criterion of 0.3, evaluated at two metres above floor level, within its occupant assessment. That is a criterion of the documented method, not a universal boundary between injury and no injury for every person.<ref name="abcb-human"/>

The occupant population matters independently of the numerical model. Purser discusses variation in susceptibility and uncertainty in predicting human responses to complex fire atmospheres. A nominal response endpoint cannot guarantee an identical response from every individual. The design interpretation must distinguish the model endpoint from the margin adopted for the assessment.<ref>Purser (2002), pp. 2-89–2-90.</ref>

The relation to [[Available safe egress time|available safe egress time]] (ASET) is therefore conditional. ASET ends when the first applicable criterion is exceeded at the specified assessment location. Heat may govern that time, but visibility or toxic exposure can become limiting earlier. Passing a thermal check does not establish that all other conditions remain tenable.<ref name="nz-tenability"/>

== Radiation while passing a window ==

[[Thermal radiation|Thermal radiation]] along an escape route provides a useful example of an explicitly defined endpoint. The supplied 2025 New Zealand method considers occupants passing a window opening or glazed panel. Its criterion requires the predicted time to onset of pain to exceed the time spent in the relevant exposure region.<ref name="nz-window">Ministry of Business, Innovation and Employment (2025), pp. 34–36, §3.7.</ref>

For that method, the time to pain is calculated from the maximum incident radiant flux using the following empirical expression. The numerical coefficient requires the stated units.<ref name="nz-equations">Ministry of Business, Innovation and Employment (2025), pp. 35–36, equations 3.6 and 3.8.</ref>

<div class="fse-equation">t<sub>p</sub> = (35/q″<sub>r</sub>)<sup>1.33</sup></div>

<div class="fse-equation">t<sub>exp</sub> = D/V</div>

{| class="wikitable"
! Symbol !! Meaning in this method !! Unit
|-
| t<sub>p</sub> || Predicted time to onset of pain || s
|-
| q″<sub>r</sub> || Maximum incident radiant heat flux || kW/m<sup>2</sup>
|-
| t<sub>exp</sub> || Exposure time while passing the window || s
|-
| D || Travel distance within the specified radiation exposure region || m
|-
| V || Assumed travel speed || m/s
|}

The method assumes a speed of 1.0 m/s. Its exposed travel distance covers the part of the route where incident radiation is at least 2.5 kW/m<sup>2</sup>. This is a specific way to define exposure for the calculation. It should not be interpreted as proof that lower fluxes have no possible effect over any duration.<ref name="nz-equations"/><ref name="purser-skin"/>

The surrounding limitations are essential. The simplified analysis applies to a single window and limits the maximum radiation to 10 kW/m<sup>2</sup>. Passage must occur within ten minutes after ignition unless fire-resisting glazing is used. The method is not appropriate where occupants are likely to have impaired mobility.<ref name="nz-window"/>

Multiple windows require a more detailed treatment of the cumulative, time-dependent exposure. The source also includes conditions concerning glazing, alternative routes and other protective provisions. Reproducing the pain equation alone does not reproduce the full verification method or establish compliance with all of its requirements.<ref name="nz-window"/>

== Worked example and sensitivity ==

Consider an illustrative maximum incident flux of 5.0 kW/m<sup>2</sup> and an exposed path length of 8.0 m. Applying the method's assumed speed gives an exposure time of 8.0 s. The pain equation gives the following result, calculated without intermediate rounding.<ref name="nz-equations"/>

<div class="fse-equation">t<sub>p</sub> = (35/5.0)<sup>1.33</sup> = 13.3 s</div>

The calculated exposure time is shorter than the predicted pain time for these selected inputs. This comparison illustrates the equation and its endpoint. It does not demonstrate that a particular route meets every requirement of the method, nor that smoke, toxicity and other exposures have been addressed.<ref name="nz-window"/><ref name="nz-tenability"/>

Increasing the maximum flux to 8.0 kW/m<sup>2</sup>, while retaining the same illustrative path and speed, reduces the calculated pain time to approximately 7.12 s. The eight-second passage would then exceed the predicted pain time. This sensitivity shows why the exposure intensity and travel duration must be assessed together.<ref name="nz-equations"/>

The two flux values are selected calculation inputs, rather than measurements of a particular fire. A project application would first establish the incident flux using the geometry and radiation procedure appropriate to the source. The occupant-response calculation cannot supply that missing fire-exposure information.<ref name="nz-window"/>

It would also be inappropriate to extend the calculation to a slower, mobility-impaired population simply by substituting a different speed. The supplied method explicitly excludes that application. A different exposure and movement assessment would be required to address the changed population and its relevant response assumptions.<ref name="nz-window"/>

The example also illustrates the importance of units. The pain equation gives seconds for flux entered in kilowatts per square metre. Substituting watts per square metre without changing the empirical coefficient changes the numerical result. The unit convention is part of the equation's definition.<ref name="nz-equations"/>

== Interpretation within an evacuation assessment ==

A thermal assessment should identify the effect being prevented, the exposure model and the occupant assumptions before interpreting a calculated time. Pain avoidance, preservation of escape capability and prevention of severe injury are related objectives, but their response criteria are not interchangeable.<ref name="purser-escape"/><ref name="purser-skin"/>

The exposure location also needs to be clear. A temperature measured within an upper gas layer does not automatically describe a person's whole exposure along an escape route. The relevant quantities must be evaluated where the selected method requires them, with any movement and shielding assumptions stated.<ref name="nz-tenability"/><ref name="nz-window"/>

Thermal and non-thermal hazards can affect the same movement. Smoke may obscure the route, irritants may impair vision or breathing, and heat may make continued passage painful. Purser's discussion of escape impairment shows why these effects must be interpreted together, even when separate numerical criteria are used.<ref name="purser-escape"/>

A useful engineering conclusion therefore reports which criterion controls, where it is exceeded and what exposure assumptions support the result. It retains the distinction between a method-specific threshold and an individual physiological outcome. This makes the calculation relevant to the evacuation decision without overstating what the thermal model predicts.<ref name="abcb-human"/><ref name="nz-tenability"/>

== See also ==
* [[Fireball]]

== Notes ==
<references/>

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method: Handbook'' (Version 1.1).
* Ministry of Business, Innovation and Employment. (2025). ''C protection from fire: Verification Method C/VM2'' (2nd ed.).
* Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-83–2-171). National Fire Protection Association.

[[Category:Smoke, Toxicity & Tenability]]

Upward flame spread

2026-11-01T23:01:17Z

Peter: New FSE wiki article: Upward flame spread (written by GPT-6)

'''Upward flame spread''' is the advance of burning along a combustible surface in an upward direction, assisted by the rising flow generated by the fire. On a vertical wall, the flow carries flame and hot gases towards material above the burning region. Quintiere classifies this as wind-aided spread: the relevant flow can be generated by buoyancy, without an external wind.<ref name="Q-250-251">Quintiere (2002), pp. 2-250–2-251.</ref>

The visible flame and the surface region supplying combustible gases have different boundaries. Flames can extend above the actively pyrolysing material and heat the unburned surface ahead. The surface spread rate describes the movement of the pyrolysis front, rather than simply the movement of the visible flame tip.<ref name="Q-246">Quintiere (2002), p. 2-246.</ref><ref name="Q-251-252">Quintiere (2002), pp. 2-251–2-252.</ref>

Upward spread can accelerate because the growing burning region increases heat release and extends the region heated by the flame. This feedback competes with burnout of material already involved. The outcome therefore depends on the material, exposure, geometry and flow. Upward orientation creates the potential for rapid growth, but does not establish one universal spread speed or growth law.<ref name="Q-252-253">Quintiere (2002), pp. 2-252–2-253.</ref>

== Heat feedback and the direction of flow ==

[[Flame spread|Surface flame spread]] requires heat to pass from the existing fire to material that has not yet become involved. For a solid, this heating produces combustible gases through thermal decomposition. Those gases burn near the surface and contribute further heat. The moving pyrolysis boundary is the material-side expression of that continuing process.<ref name="Q-246" />

In upward spread, buoyancy aligns the hot flow with the direction of advance. The flame and combustion products can heat a substantial length of surface above the pyrolysis front. In [[Opposed-flow flame spread|opposed-flow flame spread]], the flow is directed against the advance, and the region supplying forward heating is much shorter. Quintiere identifies this difference in heating extent as central to the different behaviour.<ref name="Q-247">Quintiere (2002), p. 2-247.</ref><ref name="Q-251">Quintiere (2002), p. 2-251.</ref>

Wind-aided spread is the broader category. Quintiere includes spread driven by external flow and spread beneath a ceiling within that category, as well as upward wall spread. The classification describes the relationship between the flow and the advancing front. It does not mean that all these geometries have the same flame attachment, heat transfer or spread correlation.<ref name="Q-250-251" /><ref name="Q-253" />

The relevant [[Heat flux|heat flux]] is distributed over that forward region. A high value at one location does not by itself determine the spread rate. The length exposed, duration of heating and material response also matter. Quintiere's simplified comparison explicitly includes both the flux and the distance over which it heats unburned material.<ref name="Q-251-252" />

This explains why comparing only peak heat fluxes can be misleading. Quintiere reports an orientation study in which downward spread had a higher local maximum than upward spread. The upward configuration nevertheless exposes a longer region ahead of the front. A point measurement and an extended preheating process describe different aspects of the heat feedback.<ref name="Q-254">Quintiere (2002), p. 2-254.</ref>

Ignition position can therefore change the subsequent development even when the material and pilot flame are similar. Iqbal and Salley use a curtain as an example. Ignition near its lower end permits rapid upward spread; ignition near its upper end leads to slower downward spread. The example illustrates the role of orientation and available fuel above the ignition location.<ref name="N-6-3">Iqbal and Salley (2004), p. 6-3.</ref>

== Acceleration, flame extent and burnout ==

A growing pyrolysis region can supply more fuel vapour and increase heat release. A longer flame can then heat more material ahead of the front, allowing the burning region to grow further. Quintiere relates the flame extent to heat release per unit width and uses this connection in models of upward spread. The feedback links material burning behaviour with flame geometry.<ref name="Q-252">Quintiere (2002), p. 2-252.</ref>

[[Flame height|Flame height]] therefore helps describe the region capable of heating the surface, but it must be distinguished from pyrolysis height. The flame may extend beyond the point at which the solid is producing combustible gases. Treating the flame tip as the boundary of already burning material would overstate the pyrolysing area and alter the inferred heat release.<ref name="Q-246" /><ref name="Q-252" />

Burnout introduces a second moving boundary behind the advancing front. Material that has exhausted its available fuel no longer contributes in the same way to the burning region. Quintiere represents the active region between the burnout position and the pyrolysis front. Its length can grow, approach a limit or decline, depending on the relative progress of these boundaries.<ref name="Q-252-253" />

The competition between spread time and burning duration is consequently important. If new material ignites rapidly while previously ignited material continues burning, the active region can expand. If the material burns out before sufficient new area becomes involved, growth can slow or stop. The upward direction alone does not remove this competition.<ref name="Q-246" /><ref name="Q-252-253" />

Some simplified limiting cases give exponential growth, but that result depends on particular relationships and negligible burnout. Quintiere discusses other observed and modelled behaviours, including an active region approaching a steady limit. An exponential fit should therefore be tied to its assumptions and conditions. It is not an inherent law applying to every vertical combustible surface.<ref name="Q-252-253" />

The feedback also depends on configuration. A relation between heat release and flame extent established for one arrangement is not automatically valid for another. Quintiere requires configuration-specific descriptions of flame heat flux and length when developing a spread solution. This requirement becomes important when moving from a flat wall to a corner, ceiling or constrained channel.<ref name="Q-252" /><ref name="Q-254" />

Different parts of the active surface can also be at different stages of their burning history. Quintiere combines the contributions of previously ignited regions when formulating the heat release that drives flame extent. A single peak heat release rate multiplied by the entire involved area does not preserve that timing. The history of ignition and subsequent burning is part of the feedback calculation.<ref name="Q-252" />

== A simplified relation and worked example ==

Quintiere expresses the spread speed through the distance between the pyrolysis front and the flame extent, divided by an associated ignition time. The relation connects the extent of forward heating with the time required for the heated material to become involved. It is a simplified representation, including an assumption of uniform flame heat flux over that region.<ref name="Q-252-e21">Quintiere (2002), p. 2-252, Equation 21.</ref>

<div class="fse-equation">V = dx<sub>p</sub>/dt = (x<sub>f</sub> − x<sub>p</sub>) / τ</div>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| V || Upward movement rate of the pyrolysis front || m/s
|-
| x<sub>p</sub> || Pyrolysis-front position measured from the chosen origin || m
|-
| x<sub>f</sub> || Flame extent measured from the same origin || m
|-
| t || Time || s
|-
| τ || Ignition time associated with the represented flame heat flux || s
|}

For a vertical surface, the positions can be expressed as heights above a common origin. The quantity in the numerator then represents the forward heating length in the simplified model. The associated ignition time must correspond to the heating conditions being represented. An ignition time measured under an unrelated exposure cannot be substituted merely because it is available.<ref name="Q-252" />

Consider hypothetical positions of 0.60 m for the pyrolysis front and 1.20 m for the flame extent. With an associated ignition time of 60 s, the heating length is 0.60 m. The calculated instantaneous spread speed is 0.010 m/s, or 10 mm/s. These values are selected to illustrate the relation, rather than taken from a particular material test.<ref name="Q-252-e21" />

If the flame extent becomes 1.50 m while the other example inputs remain unchanged, the heating length becomes 0.90 m. The calculated speed increases to 15 mm/s. Alternatively, retaining the original heating length but reducing the associated ignition time to 30 s gives 20 mm/s. The examples separate the influence of heating extent from that of material ignition response.<ref name="Q-252-e21" />

{| class="wikitable"
! Hypothetical comparison !! Forward heating length (m) !! Associated ignition time (s) !! Calculated speed (mm/s)
|-
| Base illustration || 0.60 || 60 || 10
|-
| Longer heated region || 0.90 || 60 || 15
|-
| Shorter ignition time || 0.60 || 30 || 20
|}

These calculations are conditional snapshots. They do not predict how flame extent, pyrolysis height or ignition response will change during a real fire. A time-dependent model requires additional relationships for heat release, heat transfer and burnout. Holding the example inputs constant throughout an assumed growth period would add a further assumption that has not been demonstrated here.<ref name="Q-252-253" />

The relation also presumes a flame extending ahead of the pyrolysis front and a positive associated ignition time. If those conditions no longer represent the fire, the simplified expression is outside its intended interpretation. A zero or negative numerator should not automatically be treated as a validated prediction of extinction or reverse spread.<ref name="Q-251-252" />

== Material response and the imposed exposure ==

Material properties enter through the heating needed to produce combustible gases and through the subsequent burning history. Quintiere distinguishes thermally thin and thermally thick behaviour in simplified spread analyses. A thin specimen can approach a uniform temperature through its thickness; a thick specimen develops a temperature gradient. The heat required to advance the front consequently depends on the relevant thermal response.<ref name="Q-248-251">Quintiere (2002), pp. 2-248–2-251.</ref>

Thickness alone is not a universal classification independent of time and exposure. Quintiere discusses the effects of thermal penetration and the adjacent substrate, particularly for intermediate thicknesses. A surface layer tested on one backing can therefore have a different heating response from the same layer in another construction. The represented material arrangement needs to accompany the material name.<ref name="Q-249">Quintiere (2002), p. 2-249.</ref>

Preheating changes the energy needed to reach the ignition condition. Van Rossum explains that upward orientation transfers heat to material above the burning region and can accelerate subsequent involvement. Additional heating in an enclosure can also raise the temperature of fuel ahead of the front. The initial surface condition is therefore part of the spread problem.<ref name="V-4-3">Van Rossum (2027), §4.3.</ref><ref name="Q-247" />

There is no single flame heat flux appropriate to every upward fire. Quintiere reports approximately 25 kW/m² ahead of the pyrolysis zone for moderate turbulent wall fires with flame extents below about 1.4 m. The same discussion shows that larger and laminar fires can exceed this value. The numerical approximation belongs to the described exposure regime.<ref name="Q-253">Quintiere (2002), p. 2-253.</ref>

Babrauskas describes a broader cluster of wall-flame measurements between approximately 25 and 45 kW/m², suggesting 35 kW/m² as representative in that context. He also notes the additional heating possible within a hot gas layer. These accounts illustrate why exposure selection needs its experimental basis and scenario conditions, rather than an unexplained universal flux assumption.<ref name="B-6-7">Babrauskas (2002), pp. 3-6–3-7.</ref>

The heat release history used in a spread calculation must correspond to that exposure. Quintiere identifies cone calorimeter data as a possible source of material burning information, while warning that the relevant flame-spread flux need not equal the selected test irradiance. The transfer from a material test to a spread model therefore requires a reasoned exposure match.<ref name="Q-252" />

== Geometry, confinement and external walls ==

A wall affects the surrounding flow as well as providing a possible combustible surface. Iqbal and Salley explain that a fuel package near a wall has less surrounding cool-air entrainment than one burning freely. This can produce higher flames and temperatures. Surface orientation and proximity to boundaries therefore influence the exposure that drives further spread.<ref name="N-6-3" />

Corners and channels can introduce additional geometric effects. Quintiere describes how escalator sidewalls in the King's Cross fire caused flames to remain close to the steps. This is the [[Trench effect|trench effect]] context cited in his discussion of orientation. It demonstrates that inclined, constrained spread can differ from the behaviour represented by an isolated vertical flat-wall model.<ref name="Q-254" />

In a [[Facade fire|facade fire]], vertical travel of flames does not necessarily mean that the cladding itself is sustaining upward surface spread. The New Zealand commentary distinguishes spread over facade materials from fire plumes projecting through openings and exposing openings above. Identifying which mechanism is active is necessary before selecting a surface-spread model.<ref name="NZ-134">Ministry of Business, Innovation and Employment (2013), p. 134.</ref>

The external-wall assembly can also behave differently from a small isolated material specimen. The commentary identifies connections and jointing details as reasons why small-scale testing may be unsuitable. A [[Large-scale facade fire test|large-scale facade fire test]] can address the behaviour of an arrangement whose relevant details are not represented by the material specimen alone. The cited commentary supports this distinction without defining one universal facade test procedure.<ref name="NZ-135-136">Ministry of Business, Innovation and Employment (2013), pp. 135–136.</ref>

== Interpreting tests and model results ==

A useful assessment identifies the measured or predicted front. Visible flame extent, pyrolysis height, burnout position and heat release describe different features of the event. Quintiere's model separates these quantities because their relationships drive the growth. Reporting only a maximum flame height can leave the actual surface involvement and its rate of advance unresolved.<ref name="Q-246" /><ref name="Q-252-253" />

A test rating is likewise not automatically a spread velocity. Quintiere describes the historical Steiner tunnel test as a complex wind-aided configuration and notes that it does not measure the pyrolysis or burnout positions. Its output cannot simply replace those variables in a physical spread equation. The test arrangement and reported quantity need to match the intended use of the data.<ref name="Q-253" />

The material, orientation, dimensions, substrate, ignition source and external heating should therefore remain explicit when interpreting a result. Quintiere concludes that spread depends on the fuel's configuration and ambient conditions as well as its properties. Applying an experimental or modelled result beyond those conditions requires evidence that the controlling heat-transfer and burning processes remain represented.<ref name="Q-256">Quintiere (2002), p. 2-256.</ref>

== Notes ==
<references />

== References ==
* Babrauskas, V. (2002). Heat release rates. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 3-1). National Fire Protection Association.
* Iqbal, N., & Salley, M. H. (2004). ''Fire dynamics tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission fire protection inspection program'' (NUREG-1805). U.S. Nuclear Regulatory Commission.
* Ministry of Business, Innovation and Employment. (2013). ''Commentary for Building Code Clauses C1–C6 and Verification Method C/VM2''.
* Quintiere, J. G. (2002). Surface flame spread. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 2-12, pp. 2-246–2-257). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Ignition & Flame Spread]]

Soot yield

2026-11-01T22:59:49Z

Peter: New FSE wiki article: Soot yield (written by GPT-6)

'''Soot yield''' is the mass of soot produced per unit mass of fuel consumed or reacted, with the precise denominator defined by the measurement or model. It is commonly expressed in kilograms per kilogram. In fire calculations, the yield connects the burning rate to a particulate source term that can subsequently be transported through a building.<ref name="definition-sfpe">Mulholland (2002), pp. 2-258–2-259.</ref><ref name="abcb-definition">Australian Building Codes Board (2020), pp. 19–20.</ref><ref name="fds-yield">McGrattan et al. (2026), pp. 52–54.</ref>

The yield is conditional on the fuel and combustion environment. It is not a fixed conversion from heat release to smoke, nor does it directly specify local visibility. Ventilation, heating and combustion efficiency affect the source term, while transport and aerosol properties affect the resulting conditions away from the fire.<ref name="abcb-ventilation">Australian Building Codes Board (2020), pp. 21–23.</ref>

Care is also needed with terminology. [[Soot|Soot]] denotes carbonaceous particles, whereas a measured smoke aerosol can include condensed droplets. Engineering sources sometimes group smoke and soot yields together. Their numerical values should therefore be interpreted with the original measurement definition and combustion conditions intact.<ref name="mulholland-formation">Mulholland (2002), pp. 2-258–2-259.</ref>

== Definition and mass basis ==

For a stated interval and a consistent fuel basis, the yield is the ratio of produced soot mass to consumed fuel mass. If that yield remains constant, the same ratio applies to the corresponding rates:<ref name="abcb-definition"/><ref name="fds-yield"/>

<div class="fse-equation">y<sub>s</sub> = m<sub>s</sub>/m<sub>f</sub></div>

<div class="fse-equation">ṁ<sub>s</sub> = y<sub>s</sub>ṁ<sub>f</sub></div>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| y<sub>s</sub> || Soot yield on the stated fuel basis || kg/kg
|-
| m<sub>s</sub> || Produced soot mass || kg
|-
| m<sub>f</sub> || Fuel mass consumed or reacted, as defined || kg
|-
| ṁ<sub>s</sub>, ṁ<sub>f</sub> || Corresponding mass production and fuel consumption rates || kg/s
|-
| Q̇ || Heat release rate consistent with the fuel consumption || kW
|-
| ΔH<sub>eff</sub> || Effective chemical heat of combustion || kJ/kg
|-
| C<sub>s</sub> || Suspended soot concentration at the location considered || kg/m<sup>3</sup>
|}

The denominator deserves explicit attention. A reaction model may define yield per mass of fuel reacted, while an experimental report may use specimen mass lost or material burnt. Those descriptions should not be silently exchanged. A calculation needs the measured or prescribed mass rate that corresponds to the stated yield.<ref name="abcb-definition"/><ref name="fds-yield"/>

Yield and production rate answer different questions. A yield of 0.03 kg/kg means that the selected mass basis produces three percent as much soot mass. It does not describe how quickly that soot appears. The production rate also requires the rate at which fuel enters the relevant combustion process.<ref name="abcb-definition"/>

For changing conditions, the total production follows the accumulation of the instantaneous source rate. A constant yield can be taken outside that accumulation only when the assumption is justified. If a fire changes from well-ventilated burning to oxygen-limited burning, a single average value can conceal different stages of particulate production.<ref name="abcb-ventilation"/>

== Formation, oxidation and combustion conditions ==

Flaming soot production reflects competing processes. Particles develop in fuel-rich regions, while oxidation can consume them where oxygen becomes available. The emitted quantity represents what survives these processes. Fuel chemistry influences formation, but the surrounding combustion environment also determines how much particulate material leaves the flame.<ref name="mulholland-formation"/>

Mulholland contrasts the relatively high smoke production of aromatic polystyrene with that of polypropylene, whose molecular structure differs. This comparison explains why fuel identity matters. It does not establish one yield for every product bearing a broad polymer name. Formulation, physical form and test conditions remain relevant when selecting a numerical input.<ref name="mulholland-formation"/>

The distinction between flaming and non-flaming aerosols is equally significant. Pyrolysis can release vapours that condense as droplets after cooling. Smouldering can sustain decomposition and produce an aerosol without an ordinary flame. Calling all these particles soot can obscure differences in composition and optical response.<ref name="mulholland-formation"/>

As an illustration, Mulholland reports flexible polyurethane smoke conversion factors of 0.07–0.15 for pyrolysis and less than 0.01–0.035 for flaming. These are results associated with small specimens and specified conditions. They describe the measured smoke aerosol; they should not be relabelled as universal elemental-carbon yields.<ref>Mulholland (2002), p. 2-259, Table 2-13.1.</ref>

Ventilation changes more than the total oxygen supplied to a room. It affects the conditions under which gases burn and particles oxidise. The ABCB data sheets describe soot yield as sensitive to both ventilation and imposed heating. Their treatment pairs increased yields under ventilation control with reduced effective heats of combustion.<ref name="abcb-ventilation"/>

The [[Equivalence ratio|equivalence ratio]] provides one way to describe the fuel-to-air balance relative to stoichiometric demand. The ABCB source presents correlation-derived yields for several values of this ratio. These data demonstrate a dependence on combustion conditions; they do not justify replacing a spatially varying fire environment with an unexplained universal multiplier.<ref name="abcb-ventilation"/>

Suppression creates a related interpretation problem. Less complete combustion can increase the particulate yield per kilogram, while a reduced burning rate decreases the fuel consumed each second. Van Rossum explains that the absolute smoke production can consequently remain limited even when the yield increases. Both factors must be examined together.<ref name="rossum-yield">Van Rossum (2027), §§6.2–6.3.</ref>

== Converting a design fire into a particulate source ==

A design fire is often specified by heat release rate rather than fuel consumption. The conversion to particulate production then requires an effective heat of combustion consistent with the combustion conditions.<ref name="abcb-definition"/>

<div class="fse-equation">ṁ<sub>f</sub> = Q̇/ΔH<sub>eff</sub></div>

<div class="fse-equation">ṁ<sub>s</sub> = y<sub>s</sub>Q̇/ΔH<sub>eff</sub></div>

With heat release in kilowatts and effective heat of combustion in kilojoules per kilogram, the resulting mass rates are kilograms per second. A value supplied in megajoules per kilogram must first be converted consistently. The equation describes a mass source, rather than the volume of hot smoke generated.<ref name="abcb-definition"/>

The ABCB definition of effective chemical heat of combustion includes combustion efficiency. It is therefore distinct from the net heat available if the fuel burns completely. Using a complete-combustion value together with a yield representing inefficient burning can produce an inconsistent conversion from energy to mass.<ref name="abcb-definition"/>

This coupling is especially important when heat release is held fixed during a sensitivity study. A lower effective heat of combustion implies that more fuel must be consumed to supply that prescribed heat release. If the yield also rises, both changes increase the calculated particulate production. Varying the yield alone misses part of this relationship.<ref name="abcb-ventilation"/>

The same reasoning applies to a total released energy. For a constant yield and effective heat of combustion, the produced mass follows from energy divided by effective heat of combustion, multiplied by yield. Van Rossum uses this energy-based approach to calculate the particulate mass available to a smoke volume.<ref name="rossum-yield"/>

A designer should therefore identify whether the starting input is fuel loss, energy release or a prescribed heat release curve. Each route can support a soot calculation, but the necessary conversion assumptions differ. Documenting those assumptions makes it possible to check that the mass and energy descriptions refer to the same fire.<ref name="abcb-definition"/><ref name="rossum-yield"/>

== Worked comparison of paired inputs ==

The ABCB data sheets provide a useful illustration using red oak. Their correlation-derived data give a well-ventilated yield of 0.015 kg/kg and effective heat of combustion of 12.4 MJ/kg. At an equivalence ratio of three, the corresponding values are 0.034 kg/kg and 6.2 MJ/kg.<ref name="abcb-tables">Australian Building Codes Board (2020), p. 22, Tables 9–10.</ref>

For an illustrative prescribed heat release of 1000 kW, the well-ventilated input pair gives a fuel rate of 0.0806 kg/s. Multiplying by the yield gives a particulate source of approximately 0.00121 kg/s, or 1.21 g/s. These are calculated values using the source's paired inputs.<ref name="abcb-definition"/><ref name="abcb-tables"/>

The second input pair gives a fuel rate of 0.161 kg/s and a particulate source of approximately 0.00548 kg/s, or 5.48 g/s. The calculated soot rate is approximately 4.53 times the first value. The increase reflects both the higher yield and the lower effective heat of combustion.<ref name="abcb-tables"/>

{| class="wikitable"
! Input condition !! Yield, kg/kg !! Effective heat, MJ/kg !! Calculated fuel rate, kg/s !! Calculated soot rate, g/s
|-
| Well ventilated || 0.015 || 12.4 || 0.0806 || 1.21
|-
| Equivalence ratio three || 0.034 || 6.2 || 0.161 || 5.48
|}

This is a controlled arithmetic comparison at fixed heat release. It is not a prediction that a real red-oak fire necessarily maintains 1000 kW as ventilation changes. Actual heat release can change with fuel supply, oxygen availability and the location of combustion. The example isolates the consequences of converting a prescribed energy source into a mass source.<ref name="abcb-definition"/><ref name="abcb-ventilation"/>

The underlying values also have a specific evidential status. The ABCB tables use correlations derived from bench-scale experiments to convert well-ventilated properties to other conditions. They are not a set of independent full-scale building measurements. Their value here is the demonstration of coupled inputs and the need to preserve their conditions of application.<ref name="abcb-tables"/>

A complementary illustrative calculation holds fuel consumption explicit. At a yield of 0.03 and a fuel rate of 0.05 kg/s, soot production is 1.5 g/s. If the yield doubles while the fuel rate falls to 0.01 kg/s, production becomes 0.6 g/s. A larger yield can therefore accompany a smaller absolute source.<ref name="abcb-definition"/><ref name="rossum-yield"/>

== Transport and optical consequences ==

The produced source must be distinguished from suspended concentration. Particles can leave a compartment with the gas flow, accumulate within a layer, or deposit on surfaces. The local concentration depends on those processes and the volume into which the source is distributed. Yield alone does not determine conditions at an occupied location.<ref name="mulholland-transport">Mulholland (2002), pp. 2-259, 2-263.</ref>

Under the restrictive assumption of complete retention and uniform mixing, concentration is soot mass divided by the receiving volume. Mulholland's room example converts 0.200 kg of fuel at a yield of 0.03 into 0.00600 kg of aerosol. Uniform distribution through 90.0 m<sup>3</sup> gives 6.67 × 10<sup>−5</sup> kg/m<sup>3</sup>.<ref name="mulholland-room">Mulholland (2002), pp. 2-265–2-266.</ref>

The source explicitly discusses why that calculation is approximate. Concentration can be higher near the ceiling, and the chosen generic foam yield may not represent the actual item. Earlier smouldering can produce a different aerosol. A uniform-room calculation should therefore retain these assumptions when its result is used elsewhere.<ref name="mulholland-room"/>

Concentration is converted to [[Optical density|optical density]] using an optical coefficient and a stated logarithm convention. A further empirical relationship is needed to estimate [[Visibility in smoke|visibility in smoke]]. These steps introduce information beyond yield, including the optical properties of the aerosol and the type of object being viewed.<ref>Mulholland (2002), pp. 2-263–2-266.</ref>

The CFAST reference illustrates this separation by transporting soot as a gaslike species and deriving optical density from its concentration. Its optical parameter is independent of the fuel-to-soot mass conversion. Changing yield modifies the source; changing the optical coefficient modifies attenuation per suspended mass. The two changes should remain distinguishable in a sensitivity assessment.<ref name="cfast-soot">Peacock et al. (2026), pp. 35–36.</ref>

Aerosol properties can also change during transport through coagulation, evaporation, condensation and deposition. These processes explain why a source measurement does not contain every detail needed to predict detector response or visibility remotely. The assumed transport representation is part of the overall smoke prediction.<ref name="mulholland-transport"/>

== Treatment in fire models ==

In [[Computational fluid dynamics|computational fluid dynamics]], a soot source may be prescribed through a reaction yield rather than obtained from a detailed particle-formation model. The supplied FDS technical reference describes this approach in its simple hydrocarbon chemistry. The user can specify soot and carbon monoxide yields, which are incorporated into the product composition.<ref name="fds-yield"/>

In that documented formulation, yield is based on mass of fuel reacted. The remaining reaction coefficients follow an atom balance. A prescribed soot yield is therefore an input to the chemical representation. A detailed gas-flow solution does not make that input an independently predicted material property.<ref name="fds-yield"/>

The supplied 2026 FDS reference states that soot and carbon monoxide yields are zero by default in this simple-chemistry formulation. Consequently, omission of a soot source in that formulation is not evidence that the represented fuel produces no smoke. The chosen reaction inputs must be checked against the intended fire description.<ref name="fds-yield"/>

This distinction also clarifies what model validation can establish. Agreement for a particular fire configuration supports the combined inputs and model treatment used for that comparison. It does not make one prescribed yield transferable to every ventilation state or fuel product. Source-data applicability remains a separate engineering question.<ref name="abcb-definition"/><ref name="abcb-ventilation"/>

The broader term [[Smoke|smoke]] should likewise not be reduced to the prescribed soot species. Gaseous products and condensed aerosols have different roles in toxicity, optical attenuation and transport. A soot input serves a particular particulate calculation; it is not a complete chemical description of the fire atmosphere.<ref name="mulholland-formation"/><ref name="fds-yield"/>

== Selecting and reporting a yield ==

Selection starts with the fuel description and the expected combustion regime. The test source should identify what was measured, the fuel mass basis, imposed heating and ventilation. Broad labels such as polyurethane or wood do not establish that two tabulated values describe equivalent materials or conditions.<ref name="mulholland-formation"/><ref name="abcb-ventilation"/>

The ABCB guidance notes the limited evidence for transferring small-scale results directly to larger fires. It also cautions that general mixed-content assumptions can be inappropriate where the contents are not well mixed. A selected representative value should therefore be connected to the relevant burning contents and assessment purpose.<ref name="abcb-definition"/><ref name="abcb-ventilation"/>

Comparative assessments can reduce sensitivity when the same assumptions apply to both a proposed design and its reference building. That does not guarantee that the ranking is unchanged. The ABCB source recommends sensitivity analysis where an alternative yield or effective heat of combustion could change the comparison.<ref name="abcb-ventilation"/>

A useful report records the selected yield, effective heat of combustion, fuel mass basis and combustion regime together. It then distinguishes produced particulate mass from transported concentration and optical consequences. This preserves the physical meaning of the source term throughout the calculation and makes the effects of alternative assumptions traceable.<ref name="abcb-definition"/><ref name="abcb-ventilation"/><ref name="cfast-soot"/>

== See also ==
* [[Fire Dynamics Simulator]]

== Notes ==
<references/>

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method data sheets: Handbook annex'' (Version 1.1).
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide. Volume 1: Mathematical model'' (6th ed., revision 6.11.1, NIST Special Publication 1018-1). National Institute of Standards and Technology.
* Mulholland, G. W. (2002). Smoke production and properties. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-258–2-268). National Fire Protection Association.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST: Consolidated model of fire growth and smoke transport, version 7. Volume 1: Technical reference guide'' (NIST Technical Note 1889v1, revision 7.7.7). National Institute of Standards and Technology.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Smoke, Toxicity & Tenability]]

VCE

2026-11-01T22:59:39Z

Peter: New FSE wiki article: Vapour cloud explosion (written by GPT-6)

#REDIRECT [[Vapour cloud explosion]]

Vapor cloud explosion

2026-11-01T22:59:34Z

Peter: New FSE wiki article: Vapour cloud explosion (written by GPT-6)

#REDIRECT [[Vapour cloud explosion]]

Jet flame

2026-11-01T22:59:28Z

Peter: New FSE wiki article: Jet fire (written by GPT-6)

#REDIRECT [[Jet fire]]

Two zone model

2026-11-01T22:59:23Z

Peter: New FSE wiki article: Zone model (written by GPT-6)

#REDIRECT [[Zone model]]

Two-zone model

2026-11-01T22:59:18Z

Peter: New FSE wiki article: Zone model (written by GPT-6)

#REDIRECT [[Zone model]]

Consolidated Fire and Smoke Transport

2026-11-01T22:59:13Z

Peter: New FSE wiki article: CFAST (written by GPT-6)

#REDIRECT [[CFAST]]

Evacuation modeling

2026-11-01T22:59:08Z

Peter: New FSE wiki article: Evacuation modelling (written by GPT-6)

#REDIRECT [[Evacuation modelling]]

Evacuation elevator

2026-11-01T22:59:02Z

Peter: New FSE wiki article: Evacuation lift (written by GPT-6)

#REDIRECT [[Evacuation lift]]

RTI

2026-11-01T22:58:57Z

Peter: New FSE wiki article: Response time index (written by GPT-6)

#REDIRECT [[Response time index]]

Response time index (RTI)

2026-11-01T22:58:52Z

Peter: New FSE wiki article: Response time index (written by GPT-6)

#REDIRECT [[Response time index]]

Neutral pressure plane

2026-11-01T22:58:47Z

Peter: New FSE wiki article: Neutral plane (written by GPT-6)

#REDIRECT [[Neutral plane]]

Window flames

2026-11-01T22:58:42Z

Peter: New FSE wiki article: External flaming (written by GPT-6)

#REDIRECT [[External flaming]]

Optical density

2026-11-01T22:58:28Z

Peter: New FSE wiki article: Optical density (written by GPT-6)

'''Optical density''' describes the attenuation of light along a path through smoke. In fire engineering, the term commonly means the base-ten optical density per unit distance, expressed in inverse metres. It connects a measured or calculated aerosol concentration with light transmission and, through an additional empirical relationship, with [[Visibility in smoke|visibility in smoke]].<ref name="mulholland-optics">Mulholland (2002), pp. 2-263–2-265.</ref>

The logarithm convention matters. Optical density per metre and the natural-logarithm extinction coefficient describe the same physical attenuation, but their numerical values differ. Neither quantity is a mass concentration, a percentage obscuration, or a direct measure of toxicity. Confusing these quantities can substantially change the interpretation of a fire calculation.<ref name="cfast-optics">Peacock et al. (2026), pp. 35–36.</ref>

A defensible application therefore identifies the optical quantity, path length, aerosol properties and intended use. Laboratory smoke measurements, predicted visibility and detector response require related information, but they do not use that information in identical ways. Particle size, lighting and the exposure of the observer remain relevant after an optical density has been calculated.<ref name="mulholland-detection">Mulholland (2002), pp. 2-265–2-267.</ref>

== Definitions and logarithm conventions ==

For a homogeneous smoke path, the transmitted fraction of monochromatic light follows the attenuation relationship given by Mulholland. The same relationship can be written with either a natural exponential or a base-ten exponential:<ref name="mulholland-optics"/>

<div class="fse-equation">I/I<sub>0</sub> = exp(−KL) = 10<sup>−DL</sup></div>

<div class="fse-equation">D = log<sub>10</sub>(I<sub>0</sub>/I)/L = K/ln(10)</div>

Here the path-integrated logarithmic attenuation is DL. Dividing by the path length produces the optical density per unit distance used throughout this article. A reported optical density is consequently incomplete unless its normalisation is clear. A dimensionless path measurement cannot be inserted directly into an equation requiring inverse metres.<ref name="mulholland-optics"/>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| I<sub>0</sub>, I || Incident and transmitted light intensity, measured consistently || Same units
|-
| L || Optical path length || m
|-
| D || Base-ten optical density per unit distance || m<sup>−1</sup>
|-
| K || Natural-logarithm extinction coefficient || m<sup>−1</sup>
|-
| K<sub>m</sub> || Mass-specific extinction coefficient, based on aerosol mass || m<sup>2</sup>/kg
|-
| C || Aerosol mass concentration || kg/m<sup>3</sup>
|-
| S || Visibility distance for a specified target and correlation || m
|}

The conversion factor is ln(10), approximately 2.303. Thus D and K are not alternative symbols for an identical number. The unit alone cannot identify the convention because both quantities have inverse-length dimensions. Model documentation and measurement reports must identify the defining equation as well as the symbol.<ref name="mulholland-optics"/><ref name="cfast-optics"/>

For example, D = 1 m<sup>−1</sup> means that a one-metre path transmits one tenth of the incident light. It does not mean complete obscuration. The exponential relationship also means that doubling the path length multiplies two transmission fractions; it does not simply double a percentage light loss.<ref name="mulholland-optics"/>

== From aerosol mass to optical attenuation ==

The extinction coefficient can be related to the mass concentration of suspended particles through a mass-specific coefficient. With the definitions above, the corresponding optical density is:<ref name="mulholland-optics"/>

<div class="fse-equation">K = K<sub>m</sub>C</div>

<div class="fse-equation">D = K<sub>m</sub>C/ln(10)</div>

This formulation separates the amount of aerosol from its optical effectiveness. The [[Soot yield|soot yield]] contributes to the amount released by the fire. The mass-specific extinction coefficient describes attenuation per unit suspended mass. Increasing either input raises the calculated optical density when the other input remains fixed.<ref name="mulholland-production">Mulholland (2002), pp. 2-258–2-259, 2-263.</ref>

The coefficient is not determined by particle mass alone. Mulholland relates extinction to particle size distribution, refractive properties and wavelength. Different aerosols can therefore produce different attenuation at the same mass concentration. The distinction is particularly relevant when comparing dark particles from flaming combustion with condensed droplets from pyrolysis or smouldering.<ref name="mulholland-production"/>

The supplied CFAST technical reference uses a default mass-specific extinction coefficient of 8700 m<sup>2</sup>/kg. It calculates layer optical density from predicted soot concentration using the logarithm conversion above. That value is a documented model parameter; it is not evidence that every fuel and combustion condition produces an identical aerosol.<ref name="cfast-optics"/>

Concentration also changes after production. Dilution and transport alter the amount of aerosol within a particular volume. Coagulation changes particle size, while deposition removes particles from the suspended phase. Condensation and evaporation can change the aerosol mass and properties. A source yield therefore does not, by itself, specify the optical conditions at a remote location.<ref name="mulholland-production"/>

This distinction prevents a common interpretation error. A high mass of [[Smoke|smoke]] produced by a fire does not specify a unique room optical density. The receiving volume, distribution, losses and optical properties must also be known. A well-mixed estimate may provide a useful calculation, but its uniform concentration is an explicit assumption.<ref name="mulholland-example">Mulholland (2002), pp. 2-265–2-266.</ref>

== Laboratory quantities and measurement practice ==

Several laboratory smoke quantities contain the words optical density. They normalise the measurement in different ways. Mulholland defines specific optical density, D<sub>s</sub>, using the chamber volume V<sub>c</sub> and exposed specimen area A:<ref name="mulholland-optics"/>

<div class="fse-equation">D<sub>s</sub> = DV<sub>c</sub>/A</div>

This quantity is dimensionless. It describes a test result normalised to specimen area, rather than the optical density per metre within an occupied space. Mulholland notes that specimen thickness affects the result. Comparing specimens therefore requires attention to the test configuration as well as the reported number.<ref>Mulholland (2002), pp. 2-263–2-264.</ref>

Mass optical density instead uses the specimen mass loss, ΔM, as the denominator:<ref name="mulholland-optics"/>

<div class="fse-equation">D<sub>m</sub> = DV<sub>c</sub>/ΔM</div>

When mass is expressed in kilograms, D<sub>m</sub> has units of square metres per kilogram of fuel lost. This denominator differs from the aerosol mass used for K<sub>m</sub>. Replacing one coefficient with the other would combine a different mass basis with a different logarithm convention. The identical dimensional form does not make the coefficients interchangeable.<ref name="mulholland-optics"/>

A direct mass optical density measurement incorporates the optical consequence of the aerosol produced during that test. A calculation using yield and mass-specific extinction instead combines two separately selected inputs. Either approach requires representative combustion conditions. Agreement between small and large tests can deteriorate when the fire becomes more complex.<ref name="mulholland-example"/>

Measurement geometry matters as well. The attenuation law is formulated for monochromatic light. Mulholland describes an extinction instrument that uses a monochromatic source and excludes forward-scattered light from the receiver. A broad-spectrum source or a receiver collecting scattered light can change the measured relationship between transmitted intensity and aerosol concentration.<ref name="mulholland-optics"/>

An engineering record should therefore preserve the original test quantity, specimen condition and mass basis. Converting every reported number into a generic smoke coefficient can conceal information needed to judge applicability. Heat flux and ventilation during the test are especially relevant because both can change smoke production.<ref name="mulholland-example"/>

== Worked calculation for a uniformly mixed room ==

Mulholland illustrates the calculation using a 200 g polyurethane foam pillow burning in a room measuring 6 m by 6 m by 2.5 m. The example selects an aerosol conversion factor of 0.03 and assumes all produced aerosol remains uniformly distributed. Its mass-specific extinction coefficient is 7.6 m<sup>2</sup>/g.<ref name="mulholland-example"/>

Using kilograms consistently gives a fuel mass of 0.200 kg, an aerosol mass of 0.00600 kg and a room volume of 90.0 m<sup>3</sup>. The resulting concentration is 6.67 × 10<sup>−5</sup> kg/m<sup>3</sup>. Converting the coefficient to 7600 m<sup>2</sup>/kg gives:<ref name="mulholland-example"/>

<div class="fse-equation">K = 7600 × (0.00600/90.0) = 0.507 m<sup>−1</sup></div>

<div class="fse-equation">D = 0.5067/ln(10) = 0.220 m<sup>−1</sup></div>

A calculated extension of the example gives a one-metre transmission of approximately 60.3%. Over five metres, transmission falls to approximately 7.94%. These values follow from the same concentration and attenuation coefficient. They illustrate why the length of the viewing path must accompany a statement about light transmission.<ref name="mulholland-optics"/>

The source also presents an alternative estimate using a fuel-based mass optical density of 0.22 m<sup>2</sup>/g. Applying that value directly to the 200 g mass loss gives D = 0.489 m<sup>−1</sup> and K = 1.13 m<sup>−1</sup>. The two routes therefore produce materially different predictions.<ref name="mulholland-example"/>

This difference is informative. The alternative calculation uses different experimental input information; it is not a correction obtained by changing the logarithm convention. Averaging the two answers would not resolve their differing assumptions. The source discusses the more direct character of the mass optical density approach while retaining the need for relevant test data.<ref name="mulholland-example"/>

The example has substantial physical limitations. Real smoke may concentrate near the ceiling, and the selected yield came from small-scale generic foam data. The pillow could smoulder before flaming, producing a different aerosol yield. The extinction coefficient also came from limited tests. The calculation is consequently an illustration of the method, not a product-specific room prediction.<ref name="mulholland-example"/>

== Visibility and the observer ==

Optical attenuation becomes a visibility estimate only after a target and a visibility relationship are selected. Mulholland presents empirical correlations of KS = 3 for a light-reflecting sign and KS = 8 for a light-emitting sign. These relationships use K, not the base-ten optical density D.<ref name="mulholland-detection"/>

For the first room calculation, the reflecting-sign relationship gives a visibility distance of approximately 5.9 m. The alternative mass optical density input gives approximately 2.7 m. Both values are calculations within the source's assumptions. Neither establishes that an occupant can necessarily identify or reach an exit at that distance.<ref name="mulholland-example"/>

Visibility depends on contrast between an object and its background. Illumination, the optical properties of the aerosol and the observer's visual acuity affect that contrast. Adaptation to dark or bright conditions also matters. An attenuation coefficient alone therefore cannot represent every aspect of visual performance during evacuation.<ref name="mulholland-detection"/>

The experimental conditions behind the correlations provide another boundary. Subjects viewed smoke through glass, which excluded the direct effect of irritants on their eyes. Irritating smoke can reduce visual acuity beyond the effect of light attenuation. Applying the optical correlation does not separately account for this physiological response.<ref name="mulholland-detection"/>

These limitations matter when selecting [[Tenability criteria|tenability criteria]]. A visibility threshold is a criterion for a specified assessment, rather than a conversion of optical density into a universal safe exposure. The visual target, lighting assumptions and required occupant task should remain identifiable in the engineering interpretation.<ref name="mulholland-detection"/>

== Percentage obscuration and detector response ==

Percentage obscuration describes the fraction of light lost over a stated path. For a one-metre reference path, the conversion from D is:<ref name="cfast-optics"/>

<div class="fse-equation">O<sub>1m</sub> = 100[1 − 10<sup>−D × 1 m</sup>]</div>

The one-metre reference is part of the definition. A percentage measured over another path cannot be converted by simply dividing that percentage by the number of metres. The transmission fractions must first be related through the exponential attenuation law. This distinction becomes increasingly significant as attenuation rises.<ref name="cfast-optics"/>

For the first room example, the one-metre obscuration is approximately 39.7%. This percentage and D = 0.220 m<sup>−1</sup> describe the same optical state. The numerical percentage is larger because it is a different expression of transmission, not because it represents a greater aerosol concentration.<ref name="cfast-optics"/>

A [[Smoke detector|smoke detector]] introduces another relationship. Light-scattering and ionisation detectors respond differently to particle size distributions. Mulholland shows that a detector's output depends on its response function and the distribution of particle sizes. Matching optical density alone does not guarantee an equal response from different detector principles or different aerosols.<ref name="mulholland-detection"/>

CFAST represents smoke detector activation by comparing layer obscuration with a specified threshold. Its technical reference describes this as a limited approach that omits transport delay and smoke penetration into the detector. A calculated threshold crossing should therefore be interpreted within that model, rather than as a complete physical simulation of detector operation.<ref name="cfast-optics"/>

== Engineering interpretation and uncertainty ==

A useful calculation keeps the full chain visible: fuel loss, aerosol yield, transport, local concentration, extinction coefficient, optical density and the final visibility or detection relationship. Uncertainty can enter at every stage. Reporting only the final distance or activation time makes it harder to identify which assumption controls the result.<ref name="mulholland-production"/><ref name="mulholland-detection"/><ref name="cfast-optics"/>

Sensitivity to the optical coefficient can be separated from sensitivity to aerosol production. Holding the room-example concentration fixed while using 8700 m<sup>2</sup>/kg gives K = 0.580 m<sup>−1</sup>. The reflecting-sign estimate then becomes approximately 5.17 m. This is a parameter comparison, not evidence that one room calculation has been validated.<ref name="cfast-optics"/><ref name="mulholland-example"/>

The CFAST formulation also illustrates a modelling boundary. Soot is transported with the gas species, and each layer has a representative concentration. That treatment provides an optical density for the modelled layer. It does not resolve every individual viewing path or the detailed particle processes that can change an aerosol during transport.<ref name="cfast-optics"/><ref name="mulholland-production"/>

A laboratory comparison needs a similarly careful boundary. An area-normalised chamber result describes the smoke produced by the exposed specimen configuration. A fuel-mass-normalised result describes optical attenuation relative to measured specimen loss. Selecting between them depends on the information required for the subsequent calculation, rather than which number appears larger.<ref name="mulholland-optics"/>

Direct mass-loss measurements have their own requirements. The sample mass change must be measured accurately alongside attenuation. An apparent improvement in the optical measurement cannot compensate for an uncertain denominator. Conversely, a reliable fuel mass loss does not establish that the smoke has the same optical properties under another ventilation condition.<ref name="mulholland-optics"/><ref name="mulholland-example"/>

These distinctions explain why a conversion between units can be exact while the resulting engineering prediction remains uncertain. The logarithmic relationship follows directly from the attenuation definitions. The relationship between a laboratory specimen and a developing room fire depends on physical representativeness. Keeping those two issues separate makes a sensitivity calculation easier to interpret.<ref name="mulholland-optics"/><ref name="mulholland-example"/>

The most useful checks are consequently definitional and physical. The logarithm, units, mass basis and optical path must agree. The selected aerosol data must suit the combustion conditions, and the assumed distribution must suit the location being assessed. These checks establish what the optical result represents before it is used in a broader fire safety decision.<ref name="mulholland-optics"/><ref name="mulholland-example"/>

== See also ==
* [[Soot]]

== Notes ==
<references/>

== References ==
* Mulholland, G. W. (2002). Smoke production and properties. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-258–2-268). National Fire Protection Association.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST: Consolidated model of fire growth and smoke transport, version 7. Volume 1: Technical reference guide'' (NIST Technical Note 1889v1, revision 7.7.7). National Institute of Standards and Technology.

[[Category:Smoke, Toxicity & Tenability]]

Fire safety concepts tree

2026-11-01T22:58:23Z

Peter: New FSE wiki article: Fire safety concepts tree (written by GPT-6)

The '''fire safety concepts tree''' is a graphical framework for relating fire safety objectives to alternative ways of preventing ignition or managing its consequences. Meacham describes it as a representation of the deliberations and professional judgements of the relevant NFPA technical committee. It provides one structured view of building fire safety and the functions needed to achieve its objectives.<ref name="M158">Meacham (2002), p. 5-158.</ref>

The two primary branches are preventing fire ignition and managing fire impact. If ignition is not prevented, the second branch directs attention to the building's ability to manage the fire and protect exposed people or things. The tree therefore connects an objective with strategies and supporting functions, rather than simply listing installed equipment.<ref name="M158" />

The framework can also help organise further analysis. The ABCB Handbook adapts part of it to show interactions among suppression, structural performance, occupant movement and fire brigade intervention. Such an adaptation needs additional information about timing, consequences and system performance before it becomes a quantitative risk assessment.<ref name="A120">Australian Building Codes Board (2020), p. 120.</ref>

== Objectives and the top-level alternatives ==

[[Fire safety objectives|Fire safety objectives]] define the outcome the strategy is intended to achieve. Meacham's wider risk framework identifies life, property, business continuity, heritage and environmental interests as possible concerns. These interests need not have identical measures of success. The objective at the top of a tree should therefore be meaningful for the assessment being undertaken.<ref name="M153">Meacham (2002), p. 5-153.</ref>

The top-level division separates prevention from management of impact. In the partial tree reproduced by Meacham, these branches form an alternative relationship. Achieving the objective requires the relevant prevention or impact-management function to succeed. This is a logical statement about the selected objective, rather than a claim that either branch always succeeds in practice.<ref name="M158" />

The prevention side identifies control of heat-energy sources, control of interactions between sources and fuel, and control of fuel. These headings direct attention to different parts of the ignition problem. They do not prescribe a particular detector, barrier or operating procedure. A project-specific assessment must identify how the relevant functions are implemented and supported.<ref name="M158" />

The impact-management side divides into managing the fire and managing those exposed. This distinction allows the assessment to examine both the development of the hazard and the circumstances of exposure. It also explains why preventing ignition is not the only route considered when a fire is already assumed to occur.<ref name="M158" />

The partial diagram in the handbook is attributed to [[NFPA]] and points to its guide for the complete tree. The diagram establishes the top-level concepts discussed here. It does not supply every lower branch, project-specific design condition or requirement that might appear in a separate edition of that guide.<ref name="M158" />

== Functions, equipment and causal sequences ==

A [[Fire safety strategy|fire safety strategy]] connects these functions with the measures available in a building. The ABCB Handbook's adaptation illustrates suppression by building users, automatic systems and the fire brigade. It also includes structural containment and occupant protection. Several measures can therefore contribute to related outcomes, while a single component can support more than one function.<ref name="A121">Australian Building Codes Board (2020), pp. 120–122, Figure 12.2.</ref>

Meacham's causal-sequence discussion provides another way to understand that distinction. It connects initiating events, outcomes, exposure and consequences. An intervention can act at different stages of this sequence. Altering the initiating conditions, blocking exposure and limiting a consequence are different forms of action, even when each contributes to the same ultimate objective.<ref name="M157">Meacham (2002), p. 5-157.</ref>

The source illustrates this with a shelter containing an open fire and obstructed ventilation. Possible interventions concern the heating arrangement, the obstruction, the fire itself or the occupants' exposure. The example shows why a strategy should identify what a measure changes. Naming the component alone does not explain its position in the causal chain.<ref name="M157" />

The tree can consequently guide an examination of a failed or unavailable function. Meacham explicitly describes evaluating fire-impact management when ignition prevention is unsuccessful. This preserves the connection with the objective while changing the conditions under consideration. It does not require pretending that the failed function remains available in the subsequent analysis.<ref name="M158" />

== Alternative and combined conditions ==

Different logical relationships occur within a strategy. Some outcomes can be achieved through alternatives, while others require several conditions together. The ABCB adaptation illustrates alternative interventions against structural collapse. Within that illustration, a successful intervention can interrupt progression towards the stated adverse outcome.<ref name="A122">Australian Building Codes Board (2020), p. 122.</ref>

The same source describes unassisted evacuation through a combined set of conditions. Detection and alarm must lead the occupant to move. Suitable movement means, a safe destination and the person's ability to evacuate without assistance are also required. Failure of a required condition can defeat that particular evacuation path.<ref name="A122" />

Movement means include capacity, route completeness, protected paths and access to the route in the Handbook's description. A warning signal alone therefore does not establish successful evacuation. The combination concerns the complete function represented in the example, including the physical route and the person using it.<ref name="A122" />

These relationships explain the connection with [[Fault tree analysis|fault tree analysis]]. Meacham places fault and event trees among methods for examining initiating events and outcomes. However, a concepts diagram does not itself provide failure rates or prove that its branches are independent. A numerical model needs those additional definitions and supporting evidence.<ref name="M158" /><ref name="A120" /><ref name="A122" />

The interpretation also depends on the objective being tested. A successful action against collapse does not automatically demonstrate that all occupants avoided harmful exposure before that action. The ABCB discussion treats frequency analysis and consequence analysis separately, with consequence criteria selected for the scenario. The logical outcome and the performance criterion must remain connected.<ref name="A122" />

== Timing and a detector-dependency example ==

The order and timing of actions affect whether a function succeeds. The ABCB Handbook warns that many outcomes in its adapted diagram depend on relative timing. A box labelled suppression therefore represents more than eventual water application. The action must occur under conditions that allow it to achieve the outcome assigned to that branch.<ref name="A120" />

Consider the detection system in the Handbook's qualitative example. Its failure can affect occupant warning, delay the call to the fire brigade and prevent linked active smoke control from operating. These effects reach different parts of the strategy, despite originating in one failed system. Drawing three separate branches does not make their initiating support independent.<ref name="A122" />

The first step in reviewing this example is to identify each function that uses the detection output. The next is to examine what the assumed failure changes in each affected sequence. For occupant movement, this includes the warning and movement conditions. For intervention and smoke control, the source identifies corresponding delays or failures of activation.<ref name="A122" />

A model that credits every affected function as available would miss the stated dependency. A model that assigns unrelated failure probabilities without examining the shared detector could also misrepresent it. The source specifically calls for these interrelationships to be considered when comparing different protection approaches in reference and proposed buildings.<ref name="A122" />

The example does not establish a numerical probability of unsuccessful evacuation or a universal delay. No such inputs have been assigned. Its purpose is to show how the concepts help expose a shared dependency before the analyst selects detailed calculations. The eventual outcome still depends on timing, remaining functions and the consequence criteria.<ref name="A120" /><ref name="A122" />

== From a concepts tree to risk assessment ==

[[Fire risk assessment|Fire risk assessment]] requires information beyond the conceptual arrangement. Meacham distinguishes the valued interest, the hazard that can cause harm and the likelihood of the unwanted outcome. The tree can help organise the relationships among these elements. It cannot supply missing frequency or consequence evidence simply through additional branches.<ref name="M153" /><ref name="M158" />

The ABCB Handbook describes combining event-tree treatment of frequencies or probabilities with deterministic analysis of selected consequences. Its adapted concepts diagram is only a partial, stylised event tree. A single action box can require a more detailed event tree of its own when the underlying operation and failure modes matter to the assessment.<ref name="A119">Australian Building Codes Board (2020), pp. 119–120.</ref>

This distinction supports proportionate detail. An analyst may begin with the top-level functions to identify relevant interactions, then develop the branches needed to examine the design question. The level of frequency analysis in the Handbook depends on the scenarios and the differences between the reference and proposed solutions. More boxes alone do not establish a better-supported result.<ref name="A120" />

A review should preserve the objective, the meaning of success and failure, shared dependencies and relevant timing assumptions. The resulting structure can then direct attention to the evidence needed for each function. Its value lies in making those connections visible while keeping the qualitative framework distinct from the calculations used to evaluate it.<ref name="M158" /><ref name="A120" /><ref name="A122" />

== Notes ==
<references />

== References ==
* Australian Building Codes Board. (2020). ''Fire safety verification method handbook'' (Version 1.1).
* Meacham, B. J. (2002). Building fire risk analysis. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 5-12). National Fire Protection Association.

[[Category:Fire Risk Analysis]]