Flame radiation

Flame radiation is the transfer of energy emitted by hot gases and particles in a flame through electromagnetic radiation. Water vapour, carbon dioxide and soot contribute to the emission and absorption occurring within a fire. Radiation can transfer heat to nearby surfaces without the flame or its hot gases touching them.

The received exposure depends on the flame's radiative properties and on the geometry between source and target. Fuel type, fire size, smoke surrounding the flame, separation distance and receiving orientation can all influence the result. The source's total radiative power and the heat flux received by a particular object are therefore different quantities. Engineering methods range from an equivalent radiation point to finite emitting surfaces and detailed radiation transport calculations. Each method combines assumptions about the source with assumptions about how its radiation reaches the surroundings.

Emission by gases and particles

Thermal radiation is produced by matter at elevated temperature. In flames, the radiating material includes both combustion gases and suspended particles. The source cannot always be represented as an opaque solid surface with one uniform temperature. Radiation is emitted and absorbed throughout a participating volume, so the path through that volume can affect the result.

Flame radiation transfers energy without requiring hot gases to reach the target. Based on Tien, Lee and Stretton (2002), chapter 1-4, p. 1-73, and Van Rossum (2027), §5.4.

Water vapour and carbon dioxide are significant radiating gases in fire calculations. Their emission and absorption vary with wavelength, with strong contributions in particular spectral bands. Different gas bands can overlap, so the total behaviour of a mixture is not found by simply adding unrelated total emissivities. The SFPE radiation chapter discusses those spectral effects and their engineering approximations.

Soot particles contribute over a more continuous range of wavelengths. The supplied Fire Dynamics Simulator reference explains why this can support a grey gas approximation for many large fire scenarios. Low soot flames may require a different spectral treatment because gas bands become relatively more influential. A flame with little visible soot consequently does not have zero thermal radiation.

Temperature, composition and path length act together. A ray crossing a larger or more strongly absorbing volume can undergo more interaction before leaving the flame. The radiation reaching an external observer is therefore influenced by both local emission and intervening absorption. A bright region inside the flame need not contribute its full emitted power to a distant target.

The flame also fluctuates in space and time. Pool flame height and visible boundaries are commonly described through mean quantities rather than instantaneous outlines. A simplified radiation calculation uses those representative dimensions and radiative properties. It does not reproduce every short lived change in the radiation field caused by the turbulent flame.

Emissive power and radiative fraction

Emissive power is radiative power emitted per unit source area. For a grey emitting representation at a uniform temperature, it can be related to blackbody emission through emissivity. The coefficient expresses departure from a perfect radiator under the stated approximation. Absolute temperature is required because the dependence is on its fourth power.

E = εσT⁴

Symbol	Description	Unit
E	Emissive power of the represented source	kW/m²
ε	Emissivity	dimensionless
σ	Stefan–Boltzmann constant in the stated power units	5.67 × 10−11 kW/(m²·K⁴)
T	Absolute source temperature	K

A representative emissivity and temperature can be difficult to establish for a real flame. Turbulent mixing produces spatial and temporal differences that a single average does not fully describe. Engineering methods therefore also use empirically determined effective emissive powers. Those values represent a whole modelled flame envelope rather than necessarily reproducing the highest local emission.

The radiative fraction instead relates total radiative power to total fire power. It is dimensionless and describes an energy division, rather than emission per unit area. A point source representation can use that fraction directly to estimate its radiative power. An emitting surface representation needs a compatible area and emissive power.

Q̇_r = χ_r Q̇

Symbol	Description	Unit
Q̇r	Total radiative power	kW
χr	Radiative fraction	dimensionless
Q̇	Actual total heat release rate	kW

Neither source quantity is automatically the exposure received by an object. A flame may emit a large total power while a distant or poorly oriented target intercepts only a small part. Conversely, a nearby target can see a substantial emitting area. The source description and receiving geometry must therefore remain separate stages of the calculation.

Source size, smoke and wind

A pool fire provides a common application for flame radiation methods. Its burning area, fuel release and burning rate influence total power and flame dimensions. The modelled size generally represents the time averaged visible envelope. For noncircular sources, an equivalent circular area is sometimes used when the original geometry is sufficiently close to circular.

A larger flame does not necessarily have a larger average emissive power per square metre. Beyler describes increasing smoke obscuration around large pool flames. Cooler smoke can screen radiation from more luminous regions inside the flame. An empirical average over the entire visible envelope can therefore decrease with pool diameter, even while the fire's total dimensions increase.

One empirical pool fire method reduces average emissive power as diameter increases. Based on Beyler (2002), chapter 3-11, p. 3-277, and Iqbal and Salley (2004), pp. 5-7 and 5-17.

The same distinction appears in the supplied Fire Dynamics Simulator treatment of local and global radiation. A nominal fraction represents emission from the flaming region, while surrounding smoke can reabsorb part of that energy. The fraction escaping the larger fire environment may therefore be smaller. This is a transport effect, rather than evidence that absorbed energy ceases to exist.

Wind can incline a flame and alter the geometry seen by a target. The source becomes closer to some locations and more remote from others. Beyler describes flame height, tilt and drag as separate geometric considerations in open fire analysis. A vertical cylinder under still air conditions cannot represent every wind affected exposure without further assumptions.

Absorption in the external atmosphere is a further process. For long distances, water vapour and other atmospheric properties can affect transmission from fire to target. This differs from absorption within the flame's own smoke mantle. The relevant path length, source characteristics and atmospheric conditions must be associated with whichever transmission treatment is adopted.

Point and finite surface methods

A point source model replaces the flame by one equivalent radiation point. Its flux varies with inverse square distance, with a further orientation factor for the receiving surface. This provides a convenient screening representation when source dimensions have relatively little influence at the target. It discards the detailed distribution of emission across the actual flame.

A solid flame model retains a finite emitting shape, often a cylinder in a still air pool fire calculation. The average emissive power is multiplied by a geometric configuration factor to obtain incident flux. The factor accounts for source size, position and receiving orientation. It is not a material emission coefficient.

q̇″ = E F

Symbol	Description	Unit
q̇″	Incident radiant heat flux at the target	kW/m²
E	Effective emissive power in the selected method	kW/m²
F	Geometric configuration factor for the selected source and target	dimensionless

The expression applies within the assumptions of the chosen surface model. It does not by itself include every possible reflection, intervening absorption or variation of surface properties. Beyler presents complete procedures that define their geometry and radiative inputs together. Their empirical components cannot be exchanged freely merely because the final equation has the same compact form.

The difference between methods matters near a fire. Beyler's pool fire comparisons show that the point representation can underpredict incident exposure in conditions where source geometry remains influential. More detailed methods retain the finite emitting envelope, although uncertainty in emissive power remains. Greater geometric detail therefore addresses one limitation without removing every source of error.

A receiving surface also exchanges radiation with its surroundings. Incident radiation is the energy arriving at it, while net radiative exchange additionally considers its own emission and the relevant surface properties. Van Rossum treats these distinctions in the heat transfer chapter. An incident flame flux should consequently not be mistaken for the net rate of heat stored in a target.

A worked emissive power example

The Shokri and Beyler treatment described in the SFPE chapter correlates effective pool flame emissive power with pool diameter. Its numerical expression uses diameter in metres and gives emissive power in kilowatts per square metre. The relationship describes an average effective flame envelope, not a measured temperature at a single point.

E = 58 × 10^{−0.00823 D}

Symbol	Description	Unit
D	Pool diameter	m
E	Effective average emissive power	kW/m²

Beyler's worked toluene example uses a pool diameter of 12 m. Inserting that diameter gives 46.20 kW/m², reported as about 46.2 kW/m². The example evaluates radiation at a ground level location 30 m from the pool centre. Its calculated maximum configuration factor is approximately 0.097 for the represented geometry.

Using the quoted configuration factor gives an incident flux of approximately 4.48 kW/m², or about 4.5 kW/m². This multiplication illustrates the distinction between source emissive power and received exposure. The source emits about 46.2 kW/m² within its effective representation, while the target receives only the geometrically weighted part. The calculation uses the rounded factor supplied by the worked example.

Geometry reduces source emissive power to the incident flux at the stated target. Based on Beyler (2002), chapter 3-11, pp. 3-286–3-287.

The factor in that example is a maximum over receiving orientation at the selected point. It is not automatically the factor for every vertical or horizontal surface located there. The chapter separately develops horizontal and vertical components before combining them. A target assessment must retain the orientation associated with the reported result.

The numerical result is an incident radiation estimate, not a statement that every material will ignite or remain undamaged. Target properties and exposure time have not been evaluated by multiplying emissive power and configuration factor. Those quantities belong to the subsequent thermal response assessment. The calculation also retains the source method's limits on pool geometry and radiative properties.

Measurement and model inputs

Effective emissive power can be inferred from measurements of radiant flux at external targets, together with an assumed flame geometry. Beyler describes fitting pool fire measurements through a cylindrical representation. The resulting value therefore reflects both the measurements and the interpretation used to connect them to the source. It is not independent of the adopted geometric model.

The average effective value can be substantially below local emission from luminous portions of the flame. A measurement directed at one bright region and a whole envelope estimate consequently concern different quantities. The same issue arises when comparing instantaneous measurements with time averaged source models. Their spatial and temporal definitions need to be retained with the reported values.

NUREG-1805 states that the empirical emissive power treatment draws on experiments with several liquid fuels, including kerosene, fuel oil, gasoline, jet fuels and liquefied natural gas. It identifies pool diameters between 1 and 50 m in the underlying experimental coverage. These conditions describe the supplied method's evidence base. They do not establish a universal radiation correlation for every small flame or complex fuel assembly.

Detailed field calculations require a different set of inputs, including gas and soot properties and their distribution through the domain. The supplied Fire Dynamics Simulator reference explains that finite calculation cells average the flame's temperature structure. Because emission depends on the fourth power of temperature, this averaging requires special treatment in the reacting region. Numerical radiation modelling therefore also contains approximations beyond the transport geometry.

Scale is relevant when interpreting laboratory measurements. The SFPE radiation chapter notes that reducing fire scale can reduce the proportion of radiation relative to other heat transfer modes. A small experimental flame can therefore represent a different energy balance from a larger fire involving similar material. Scaling dimensions alone does not establish that the radiative fraction or average emissive power remains unchanged.

Uses and limits in fire assessment

Radiation can expose adjacent combustibles and equipment while the main hot gas flow rises elsewhere. NUREG-1805 discusses such situations in large nuclear plant spaces, including equipment and cable targets. Its methods belong to that inspection and hazard analysis context. The physical distinction between lateral radiation and rising hot gases nevertheless explains why plume temperature alone does not specify every nearby exposure.

Open hydrocarbon fire assessments consider source dimensions, duration and proximity together with the receiving object's thermal characteristics. A source can present different exposures at different locations or orientations. The total radiative output is therefore insufficient to define one universal hazard distance without a stated target and criterion. Beyler structures the analysis around those separate source and receiver descriptions.

An exposed object also takes time to heat. Its dimensions, density and thermal properties influence its response to a given flame exposure. The US guidance cautions against assuming that an object beside a flame immediately reaches the flame temperature. A radiation assessment therefore separates the source field from the time dependent behaviour of the particular receiving material.

Finally, the chosen method must remain consistent across burning rate, flame geometry and radiative properties. A plausible number from one empirical model does not automatically improve another. Uncertainty includes the scenario inputs and the applicability of the representation itself. The source methodology and its experimental context remain necessary parts of interpreting the calculated flux.

See also

• Flame
• View factor
• Stefan-Boltzmann law

References

• Beyler, C. L. (2002). Fire hazard calculations for large, open hydrocarbon fires. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-268–3-314). 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.
• 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 FDS-6.11.1; NIST SP 1018-1). National Institute of Standards and Technology.
• 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.