Thermal radiation

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

$$E_s={\epsilon }_s\sigma T_s^4$$

Symbol	Description	Unit
$E_s$	Source radiant emission per unit area	W/m²
${\epsilon }_s$	Effective source emissivity	Dimensionless
$\sigma$	Stefan–Boltzmann constant, $5.67\times 10^{-8}$	W/(m²·K⁴)
$T_s$	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.

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.

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.

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.

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.

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.

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.

$$G_{\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}=F_{r\to s}{E}_s$$

Symbol	Description	Unit
$G_{\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}$	Direct source radiation incident on the receiver	W/m²
$F_{r\to s}$	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.

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.

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.

$$E_s=0.9\times 5.67\times 10^{-8}\times 673.15^4\approx 10.5\mathrm{k}\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}$$

$$G_{\mathrm{d}\mathrm{i}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{t}}=0.832E_s\approx 8.72\mathrm{k}\mathrm{W}/{\mathrm{m}}^{\mathrm{2}}$$

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.

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.

$${\dot{q}}^{\prime }{\text{'}}_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{n}\mathrm{e}\mathrm{t}}={\alpha }_r{G}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}-{\epsilon }_r\sigma T_r^4$$

Symbol	Description	Unit
${\dot{q}}^{\prime }{\text{'}}_{\mathrm{r}\mathrm{a}\mathrm{d},\mathrm{n}\mathrm{e}\mathrm{t}}$	Net radiative heat flux into the receiver	W/m²
${\alpha }_r$	Effective receiver absorptivity for the incident radiation	Dimensionless
$G_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}$	Total radiation incident on the receiver	W/m²
${\epsilon }_r$	Receiver emissivity	Dimensionless
$T_r$	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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

See also

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

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.