Heat transfer

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.

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.

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.

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.

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.

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.

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.

$${\dot{q}}^{\prime }{\text{'}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}}=\frac{\lambda }{L}(T_{s,h}-T_{s,c})$$

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.

$${\dot{q}}^{\prime }{\text{'}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}=h_c(T_g-T_s)$$

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.

$$E_r=\epsilon \sigma T^4$$

Symbol	Description	Unit
${\dot{q}}^{\prime }{\text{'}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{d}},{\dot{q}}^{\prime }{\text{'}}_{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{v}}$	Conductive and convective heat flux	W/m²
$\lambda$	Material thermal conductivity	W/(m·K)
$L$	Material thickness	m
$T_{s,h},T_{s,c}$	Hot and cold solid-surface temperatures	K or °C
$h_c$	Convective heat-transfer coefficient	W/(m²·K)
$T_g,T_s$	Gas and receiving-surface temperatures	K or °C
$E_r$	Source radiant emission per unit area	W/m²
$\epsilon$	Source emissivity	Dimensionless
$\sigma$	Stefan–Boltzmann constant, $5.67\times 10^{-8}$	W/(m²·K⁴)
$T$	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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

$$\mathrm{\Delta }E=m{c}_p\mathrm{\Delta }T$$

Symbol	Description	Unit
$\mathrm{\Delta }E$	Increase in stored thermal energy	J
$m$	Heated mass	kg
$c_p$	Specific heat capacity	J/(kg·K)
$\mathrm{\Delta }T$	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.

$$\mathrm{\Delta }E=100\times 460\times 100=4.6\times 10^6\mathrm{J}=4.6\mathrm{M}\mathrm{J}$$

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.