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Contents
  1. 1Definition and units
  2. 2Heat flux and total heat flow
  3. 3How heat flux arises
  4. 4Typical values in fires
  5. 5Effects on people
  6. 6Ignition, testing and fire spread
  7. 7Measurement and limits
  8. 8See also
  9. 9Notes
  10. 10References

Heat flux is the rate of heat transfer per unit area of a surface, measured normal to the direction in which the heat flows. It is the total of the heat transmitted by radiation, conduction and convection.[1] Its unit is the watt per square metre (W/m²), and in fire safety engineering it is usually given in kW/m².[2] Multiplying the heat flux by the area that receives it gives the total heat flow in watts.[2]

Heat flux links a fire to its effects. It sets how quickly the skin of a person heats up, whether a nearby object ignites and how fast a wall, a roof or a steel beam warms.[3][4] Below a material-specific critical heat flux, a combustible material does not ignite at all.[5] Engineers therefore use heat flux in tenability criteria, in ignition and fire spread analysis, in fire tests such as the cone calorimeter and in regulations on fire spread between buildings.

The values met in fires span a wide range. Skin can tolerate a radiant heat flux below about 2.5 kW/m² for several minutes, while a flux of 10 kW/m² becomes intolerable within seconds.[6] Small flames heat adjacent objects with 30–40 kW/m², and a post-flashover room fire exposes its walls and contents to about 150 kW/m².[7][8]

Definition and units

Heat transfer is the transport of energy caused by a difference in temperature. Heat keeps flowing from the hotter to the colder material until the temperatures are equal.[3] The heat flux describes how intense this flow is at a surface. Introduction to Fire Safety Engineering calls it the heat flow density, with the symbol q˙″ and the unit W/m².[2]

The heat flux at a surface can be incoming or outgoing. The incident heat flux is the flux arriving at a surface. A heated surface also loses part of that heat again by radiation and convection, so the net heat flux absorbed by the surface is smaller.[9] The difference matters most when the exposed surface becomes hot, because the re-radiated flux grows with the fourth power of the surface temperature.[9]

The same unit, W/m² or kW/m², is also used for the heat release rate per unit area of a burning surface. That quantity describes how much fire power a square metre of burning fuel produces, not how much heat a surface receives.[10] A fire of 1 MW with a heat release rate per unit area of 250 kW/m² covers 4 m².[10] Introduction to Fire Safety Engineering uses the symbol q˙″ for both quantities, so they are easily confused.[10][2]

Heat flux and total heat flow

The heat flux and the total heat flow through a surface are related by the area of that surface. The heat flux describes the intensity of the exposure, while the total heat flow describes the power that is transferred.[11] Introduction to Fire Safety Engineering uses this relation after first calculating the heat flux through one square metre of a construction:[2]

Q˙=q˙″⋅A

Symbol Description Unit
Q˙ total heat flow through or onto the surface W
q˙″ heat flux (heat flow density) W/m²
A area of the surface m²

The relation assumes that the heat flux is the same over the whole area.[2] The book's hand calculations also assume a steady state, in which temperatures do not change over time.[3] Such calculations are simplifications, mainly useful to estimate the order of magnitude of the heat flow.[3]

A worked example in Introduction to Fire Safety Engineering shows how the relation is used. A building of 35 m by 48 m has a steel roof 4 mm thick, a smoke layer of 634 °C below the roof and an outdoor temperature of 20 °C.[2] With surface resistances of 0.04 m²·K/W on both sides, the heat flux through the roof is about 7,670 W/m². Over the roof area of 1,680 m², the heat flow out through the roof is about 12.9 MW.[2] This is the maximum value, because it assumes a steady state, a uniform smoke layer temperature and the whole roof exposed.[2] If the roof is insulated with 100 mm of polyurethane foam, a smoke layer of 400 °C and an outdoor temperature of 10 °C drive only about 129 W/m² through it.[2]

Building section with a 634 °C smoke layer under a thin steel roof; 7,670 W/m² through one square metre times 1,680 m² gives 12.9 MW.
Worked example: a smoke layer of 634 °C under a 4 mm steel roof gives a heat flux of about 7,670 W/m²; over 1,680 m² of roof this is about 12.9 MW. Based on Van Rossum (2027), §5.2.

How heat flux arises

Heat can reach a surface in three ways: by conduction through a material, by convection from a moving gas or liquid, and by radiation through electromagnetic waves.[3] In conduction, the heat flux is proportional to the temperature gradient and points in the direction of decreasing temperature. This is Fourier's law.[12] For a single layer, the flux equals the thermal conductivity times the temperature difference across the layer, divided by its thickness.[2]

A wall heated from the left by a flame and hot smoke, with arrows for radiation and convection to the surface and conduction through the wall; one square metre is marked.
Heat flux onto and through a wall: radiation from the flame and the smoke layer, convection from hot gases along the surface and conduction through the wall. The heat flux is the heat flow per square metre, in W/m² or kW/m². Based on Van Rossum (2027), §5.1–§5.4.

In convection, the heat flux from a gas to a surface equals a heat transfer coefficient multiplied by the difference between the gas and surface temperatures.[11][13] The coefficient depends on the flow along the surface. Introduction to Fire Safety Engineering gives guide values of 1–5 W/(m²·K) for normal indoor conditions and 20–25 W/(m²·K) for a fully developed fire. For a very hot fire it gives 50 W/(m²·K). A value of 25 W/(m²·K) is usually assumed for a standard fire.[2] Convected heat can ignite easily ignitable materials far from the fire.[11]

Thermal radiation needs no medium and becomes dominant at high temperatures, because the emitted flux rises with the fourth power of the absolute temperature.[14] The flux that a target receives equals the source radiation multiplied by the view factor, which expresses how much of the source the target sees.[14] In an open fire, about 70 % of the heat leaves by convection and about 30 % by radiation.[11] Flames transfer heat to adjacent surfaces mainly by convection and radiation.[4] Radiation is the dominant mode in flames larger than about 0.2 m, while convection is more significant in smaller flames.[15]

Typical values in fires

Babrauskas compiled heat fluxes measured in real building fires to guide the choice of test conditions. For flames from a 0.3 kW Bunsen-type burner up to a 50 kW wastebasket, the peak heat fluxes to adjacent objects were remarkably constant at 30–40 kW/m².[7] A larger source did not give a higher peak flux, only a larger area exposed to it. Larger gas burners gave mostly 30–50 kW/m², in some cases 65–80 kW/m², and high-velocity jet flames 150–300 kW/m².[7] Lattimer reports peak wall heat fluxes from propane burner fires of 50–520 kW that grow with the heat release rate. The authors attributed this to the thicker boundary layers of larger fires, which lengthen the radiation path.[9]

Before flashover, heat fluxes in a room vary widely with position. Söderbom found values typically below 45 kW/m² at the centre of the ceiling. At floor level the flux stays below 20 kW/m² before flashover, because reaching 20 kW/m² at floor level is one definition of flashover.[7] Introduction to Fire Safety Engineering connects this to the smoke layer. A hot layer above 500 °C radiates about 20 kW/m², and at that flux many materials on the floor pyrolyse rapidly.[16] On burning walls, the flux from the flame to the surface just ahead of it lies mostly between 25 and 45 kW/m², with 35 kW/m² as a representative mean.[7]

After flashover, gas temperatures reach about 1100 °C. A black body at that temperature would produce about 200 kW/m², and measured fluxes in post-flashover room fires come close to this value but are usually somewhat lower.[8] A flux of about 150 kW/m² represents the post-flashover environment.[8] A burning item also heats itself through its own flame. For polymethyl methacrylate (PMMA) burning horizontally in the cone calorimeter, this flame flux is about 35 kW/m², and for fabric and foam composites 20–25 kW/m².[8]

Range chart on a log scale from 1 to 300 kW/m²: skin limit 2.5, ignition of wood 10, small flames 30 to 40, flashover floor 20, post-flashover 150 to 200, jet flames 150 to 300.
Typical heat fluxes in fires, from the tenability limit for skin to jet flames. Based on Purser (2002), p. 2-129; Tewarson (2002), p. 3-87; Babrauskas (2002b), pp. 3-6–3-7; Van Rossum (2027), §7.7.

Effects on people

The effect of radiant heat on people depends strongly on both the heat flux and the exposure time.[17] Purser gives a tenability limit for exposure of the skin to radiant heat of about 2.5 kW/m². Below this level, exposure can be tolerated for at least several minutes. At this level and above, radiant heat causes skin pain followed by burns within a few seconds. For occupants passing under a hot smoke layer, this flux corresponds to a layer temperature of about 200 °C.[6]

His table of limiting conditions gives tolerance times of more than 5 minutes below 2.5 kW/m², 30 s at 2.5 kW/m² and 4 s at 10 kW/m².[6] Radiant heat in fires tends to be directional, so the main hazard is local heating of exposed areas of skin.[6] More detail on burns and pain is given in effects of heat on people.

Introduction to Fire Safety Engineering describes the values used in the Netherlands. In Dutch fire safety engineering practice, 2.5 kW/m² is usually applied for escape and 1 kW/m² for prolonged stay.[17] The explanatory note to the Dutch building regulations (Bbl) on non-enclosed spaces uses a limit of 2 kW/m² below the smoke layer.[17] The zone model CFAST ignores radiant fluxes below 2.5 kW/m² when it calculates the fractional effective dose of heat, consistent with ISO 13571.[18]

In New Zealand, C/VM2 (second edition, 2025) limits the radiation to which occupants passing a window on an escape route may be exposed to 10 kW/m².[19] The time to the onset of pain must be longer than the time for which the occupant is exposed. All occupants must have passed the window within 10 minutes of ignition, unless fire-resisting glazing is used.[19] An occupant counts as exposed while the incident radiation exceeds 2.5 kW/m², and the exposure time follows from a walking speed of 1 m/s.[20]

Ignition, testing and fire spread

The critical heat flux for ignition is the minimum heat flux at or below which a material cannot produce a combustible mixture of vapour and air.[5] It is found by exposing samples to decreasing heat fluxes until no ignition occurs within about 15 minutes.[21] Tewarson lists critical heat fluxes of 10 kW/m² for newspaper, red oak and Douglas fir, 11 kW/m² for PMMA, 13 kW/m² for polystyrene and 15 kW/m² for polypropylene.[22] For electrical cables in US nuclear power plants, NUREG-1805 gives measured critical heat fluxes of 15–25 kW/m². For screening it uses 10 kW/m² for qualified and 5 kW/m² for unqualified cables.[1]

Above the critical value, the time to ignition falls as the heat flux rises. For thermally thick materials, the inverse of the square root of the ignition time increases linearly with the excess of the external heat flux over the critical heat flux.[21] With Tewarson's data for blackened PMMA, this gives an ignition time of about 380 s at 25 kW/m² and about 49 s at 50 kW/m².[22]

Fire tests control the heat flux on the sample. The cone calorimeter exposes a specimen to an irradiance of 0 to 110 kW/m² from an electric heater.[23] For objects ignited by a small flame, Babrauskas suggests a test irradiance of 35 kW/m². Testing for post-flashover conditions requires more than 75 kW/m², preferably close to 100 kW/m².[7][24]

Regulations on fire spread between buildings are also written in heat flux. New Zealand Building Code clause C3.6, quoted in C/VM2 (2025), limits the received radiation to 30 kW/m² at the relevant boundary and 16 kW/m² at 1 m beyond it.[25] External walls closer than 1 m to the boundary must use materials that do not ignite for 15 or 30 minutes under 30 kW/m², depending on the importance level.[25] The design emitted flux from unprotected areas ranges from 83 to 144 kW/m² in unsprinklered firecells.[26] The commentary notes that ordinary timber claddings ignite in less than 15 minutes at 30 kW/m² in the ISO 5660 test.[27]

Measurement and limits

Most heat flux data from fire experiments are total heat fluxes measured with water-cooled gauges. Their surface is painted black, with an emissivity of about 0.95, and cooled to 20–80 °C.[4] Because the gauge is much colder than a real heated material, it receives more convective and radiative heat. The measured value is therefore a conservative estimate of the heat flux to most surfaces.[4] In a worked example by Lattimer, a gauge reads 30 kW/m², but the incident flux on a wall surface at 600 K is only about 20.5 kW/m².[9]

Two surfaces beside a flame: a cooled black gauge receiving 30 kW/m² and a 600 K wall surface taking up 20.5 kW/m² after re-radiation.
Heat flux measured by a water-cooled gauge (30 kW/m²) compared with the flux taken up by a wall surface at 600 K (about 20.5 kW/m²) in the same flame. Based on Lattimer (2002), pp. 2-269–2-270.

Hand calculations of heat flux are mostly steady-state estimates. A real fire is transient: the fire grows, and the temperatures at the source and the target keep changing.[3] In the first phase of a fire, a steady calculation can overestimate the heat flow through a thick wall, because the heat has not yet reached its back face.[2] Material properties also change with temperature, so calculations with fixed properties are approximations.[2]

A common misconception is that the hottest theoretical flame sets the realistic upper bound. A black body at an adiabatic flame temperature of about 2300 K would emit some 1500 kW/m². This is nearly ten times the maximum found in normal building fires.[7] Another misconception is that a larger ignition source always produces a higher peak flux. For small sources, a larger flame mainly enlarges the area exposed to roughly the same peak flux.[7]

See also

Notes

  1. ↑ 1.0 1.1 Iqbal and Salley (2004), p. 5-2.
  2. ↑ 2.00 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11 2.12 2.13 Van Rossum (2027), §5.2.
  3. ↑ 3.0 3.1 3.2 3.3 3.4 3.5 Van Rossum (2027), §5.1.
  4. ↑ 4.0 4.1 4.2 4.3 Lattimer (2002), p. 2-269.
  5. ↑ 5.0 5.1 Tewarson (2002), p. 3-82.
  6. ↑ 6.0 6.1 6.2 6.3 Purser (2002), p. 2-129.
  7. ↑ 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Babrauskas (2002b), p. 3-6.
  8. ↑ 8.0 8.1 8.2 8.3 Babrauskas (2002b), p. 3-7.
  9. ↑ 9.0 9.1 9.2 9.3 Lattimer (2002), p. 2-270.
  10. ↑ 10.0 10.1 10.2 Van Rossum (2027), §4.6.
  11. ↑ 11.0 11.1 11.2 11.3 Van Rossum (2027), §5.3.
  12. ↑ Atreya (2002), p. 1-46.
  13. ↑ Atreya (2002), p. 1-47.
  14. ↑ 14.0 14.1 Van Rossum (2027), §5.4.
  15. ↑ Tien et al. (2002), p. 1-73.
  16. ↑ Van Rossum (2027), §4.7.
  17. ↑ 17.0 17.1 17.2 Van Rossum (2027), §7.7.
  18. ↑ Peacock et al. (2026), p. 37.
  19. ↑ 19.0 19.1 Ministry of Business, Innovation and Employment (2025b), p. 34.
  20. ↑ Ministry of Business, Innovation and Employment (2025b), p. 36.
  21. ↑ 21.0 21.1 Tewarson (2002), p. 3-83.
  22. ↑ 22.0 22.1 Tewarson (2002), p. 3-87.
  23. ↑ Babrauskas (2002a), p. 3-63.
  24. ↑ Babrauskas (2002a), p. 3-65.
  25. ↑ 25.0 25.1 Ministry of Business, Innovation and Employment (2025b), p. 43.
  26. ↑ Ministry of Business, Innovation and Employment (2025b), p. 44.
  27. ↑ Ministry of Business, Innovation and Employment (2013), p. 133.

References

  • Atreya, A. (2002). Convection heat transfer. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-44–1-72). National Fire Protection Association; Society of Fire Protection Engineers.
  • Babrauskas, V. (2002a). The cone calorimeter. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-63–3-81). National Fire Protection Association; Society of Fire Protection Engineers.
  • Babrauskas, V. (2002b). Heat release rates. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-1–3-37). National Fire Protection Association; Society of Fire Protection Engineers.
  • 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, Office of Nuclear Reactor Regulation.
  • Lattimer, B. Y. (2002). Heat fluxes from fires to surfaces. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-269–2-296). National Fire Protection Association; Society of Fire Protection Engineers.
  • Ministry of Business, Innovation and Employment. (2013). Commentary for Building Code clauses C1–C6 and Verification Method C/VM2.
  • Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
  • Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
  • Purser, D. A. (2002). Toxicity assessment of combustion products. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-83–2-171). National Fire Protection Association; Society of Fire Protection Engineers.
  • Tewarson, A. (2002). Generation of heat and chemical compounds in fires. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 3-82–3-161). National Fire Protection Association; Society of Fire Protection Engineers.
  • Tien, C. L., Lee, K. Y., & Stretton, A. J. (2002). Radiation heat transfer. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), SFPE handbook of fire protection engineering (3rd ed., pp. 1-73–1-89). National Fire Protection Association; Society of Fire Protection Engineers.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
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