Skip to content
Upcoming courses

Heat release rate per unit area

Tools
From Fire Safety Academy Wiki
Revision as of 23:36, 1 November 2026 by Daan (talk | contribs) (New FSE wiki article: Heat release rate per unit area (written by Claude Opus 5.5))
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Contents
  1. 1Definition
  2. 2Relation between heat release rate and fire area
  3. 3Typical values
  4. 4Measurement
  5. 5Use in design fires and fire models
  6. 6Limits and common misconceptions
  7. 7See also
  8. 8Notes
  9. 9References

The heat release rate per unit area is the heat release rate of a fire divided by the area that is burning. It says how intensely a fire burns on each square metre of fuel surface or floor.[1][2] It is usually written as q̇″ and expressed in kilowatts per square metre (kW/m2). Other names in the sources are heat release rate density, rate of heat release per unit area of fire and, in fire simulation software, HRRPUA.[1][3][4]

The quantity links the size of a fire to its power. When the heat release rate per unit area and the burning area are known, the total heat release rate follows by multiplication, and the reverse also holds.[1] Introduction to Fire Safety Engineering gives about 250 kW/m2 for a developed fire in an average building other than storage.[5] Measured values range from about 100 kW/m2 for some cable insulation to several thousand kW/m2 for liquid pools and high stacks of wood pallets.[6][7] Engineers use it to set the area of a design fire in fire models, to estimate the diameter of a fire for plume and flame calculations, and to estimate how long fuel can burn.[8][9][10]

Definition

Introduction to Fire Safety Engineering defines the heat release rate density as the amount of power released per unit area. In a fire it means how much heat release rate is produced per square metre of burning surface, so it says something about how intensely a fire burns on a given area.[1] The documentation of the OZone software defines it in the same way, as the energy released by one square metre of fire per second.[2] A small fire with a high value can be locally very intense, while a larger fire with a lower value spreads the same power over a wider area.[1]

The area in the definition is not always the same. For pools, spills and cone calorimeter specimens it is the area of the fuel surface itself.[11] For fuel arrays such as storage or wood pallets, the tables usually give the heat release rate per unit floor area covered by the fuel.[12][10] In compartment fire models such as OZone, the area is the floor area on which fuel is burning, and the maximum fire area is the floor area on which combustible material is present.[3] A value per unit floor area of a high storage rack can therefore be much larger than a value per unit exposed surface.

The heat release rate of a fire equals the mass burning rate of the fuel times its effective heat of combustion.[13] Per unit area, the heat release rate per unit area is therefore the burning rate per square metre multiplied by the effective heat of combustion.[14] The effective heat of combustion is lower than the value from a bomb calorimeter, because combustion in a real fire is incomplete.[13] In the OZone design fire, the effective heat release rate per unit area is defined as the maximum that can be released per unit area of fire in a steady state. It assumes that the available ventilation does not limit the fire, and it already accounts for incomplete combustion.[3]

Relation between heat release rate and fire area

The basic relation is a simple product. The heat release rate of a fire equals its heat release rate per unit area times its burning area.[1][15] It can be rearranged to give the fire area from a known heat release rate, or the heat release rate per unit area from a measured fire.[1]

Q˙=q˙″A

Symbol Description Unit
Q˙ heat release rate of the fire kW
q˙″ heat release rate per unit area kW/m2
A burning area of the fire m2

The relation holds at every moment of a fire if both the area and the heat release rate per unit area are known at that moment. Design methods usually keep the heat release rate per unit area constant, so that any change in heat release rate is caused by a change in burning area.[16] The relation describes a fire that is not limited by ventilation. Once the fire becomes ventilation controlled, the heat release rate inside the room is set by the air supply instead.[3][13]

Introduction to Fire Safety Engineering gives a simple example. A fire of 1,000,000 W with a heat release rate per unit area of 250,000 W/m2 has a burning area of 4 m2.[1] A circle with this area has a diameter of about 2.3 m. Heskestad used this approach for storage fires. He took the fire diameter as that of a circle whose area equals the heat release rate divided by the heat release rate per unit area.[9]

A second worked example comes from New Zealand. C/VM2 (second edition, 2025) sets a peak heat release rate of 20 MW for most buildings. It gives 250 kW/m2 for use in a zone model and a range of 500 to 1,000 kW/m2 for a computational fluid dynamics (CFD) model.[8] With 250 kW/m2, the fully grown design fire covers 20,000 / 250 = 80 m2. With 500 and 1,000 kW/m2, the same fire covers 40 m2 and 20 m2, a square of about 6.3 m and 4.5 m wide.

Liquid spills give a third example. In the SFPE Handbook, Gottuk and White consider 208 litres of gasoline spilled across a warehouse floor, with an estimated burning area of 116 m2. For an unconfined spill they take one-fifth of the maximum pool burning rate, 0.011 kg/(m2·s), with a heat of combustion of 43.7 MJ/kg.[17] The heat release rate per unit area is then about 480 kW/m2, and the fire reaches 0.011 × 116 × 43.7 = 56 MW.[17]

Typical values

Values depend strongly on the type of fuel and its arrangement. The Fire Dynamics Tools of the US Nuclear Regulatory Commission collect measured values for fuels found in nuclear power plants. The table gives a selection, together with the general design values of Introduction to Fire Safety Engineering and C/VM2.[18]

Fuel or situation Heat release rate per unit area (kW/m2) Source
Fire-retardant treated plywood 81 Iqbal and Salley (2004), p. 2-22
Douglas fir plywood 124 Iqbal and Salley (2004), p. 2-22
Cable jacketing PE/PVC 590 Iqbal and Salley (2004), p. 2-20
Polyurethane 710 Iqbal and Salley (2004), p. 8-3
Polyethylene 1,408 Iqbal and Salley (2004), p. 8-3
Wood pallets stacked 1.5 ft (0.46 m) high 1,420 Iqbal and Salley (2004), p. 2-22
Wood pallets stacked 10 ft (3.05 m) high 6,800 Iqbal and Salley (2004), p. 2-22
Diesel oil 1,985 Iqbal and Salley (2004), p. 2-21
Gasoline 3,290 Iqbal and Salley (2004), p. 2-21
Developed fire in an average building other than storage 250 Van Rossum (2027), §4.5
Design fire in a zone model, New Zealand 250 Ministry of Business, Innovation and Employment (2025b), p. 20
Design fire in a CFD model, New Zealand (storage) 500 to 1,000 (1,000 to 2,500) Ministry of Business, Innovation and Employment (2025b), p. 20

Several patterns stand out. Liquid fuels give much higher values than plywood or cable insulation.[19][7] For stacked fuels the value per unit floor area rises with stack height, from 1,420 kW/m2 for pallets 1.5 ft high to 10,200 kW/m2 for pallets 16 ft high.[7] Heskestad likewise uses 4,000 kW/m2 for a fully involved storage 3 m deep, and notes that methyl alcohol gave 500 kW/m2 against 2,500 kW/m2 for heptane in the same example.[20]

Introduction to Fire Safety Engineering also lists values per type of use, taken from the Dutch national annex to EN 1991-1-2. Most uses, including dwellings, offices, hotels, classrooms and health care, receive 250 kW/m2. Theatres and cinemas, libraries and retail such as supermarkets and DIY stores receive 500 kW/m2, and storage receives 500 kW/m2 per metre of storage height.[21] The book stresses that these are normative values for the assessment of structures. For a conservative model of the first phase of a fire, such as in an escape analysis, variant calculations with higher values may be needed.[21]

Thin liquid spills burn much less intensely than deep pools. Putorti and co-workers found that gasoline spills on smooth floors gave only about one-fifth of the value expected for deep pools, which in the same size range would reach about 1,900 to 2,400 kW/m2. On carpets the value was about 70% to 80% of the deep-pool value.[22] Gottuk and White therefore suggest estimating unconfined spills at one-fifth of the maximum pool burning rate. For large continuous releases, above about 10 litres per minute, they recommend the full pool rates as a conservative choice.[14]

Measurement

The heat release rate per unit area of a material is measured at bench scale with the cone calorimeter. The instrument uses oxygen consumption calorimetry to determine the heat release rate of a specimen of 100 mm by 100 mm. The specimen is normally horizontal and face up, and a conical heater exposes it to a heat flux between 0 and 110 kW/m2.[23] Its measuring functions also include the mass loss rate and the effective heat of combustion, which together explain the measured heat release.[23]

Bench-scale values do not transfer directly to large fires. The size of the specimen affects the result, because flames over larger specimens are thicker and radiate more strongly. For horizontal PMMA, each doubling of the specimen area raised the heat release rate per unit area by about 10%.[24] For liquid pools, the diameter must exceed about 1 m before the size effect becomes negligible. Vertical PMMA walls showed a rate that kept rising roughly linearly with height up to the largest height tested, 3.56 m.[24]

Full-scale values come from burning whole items or arrays under a large hood. NFPA 204M, cited by Heskestad, gives tables of heat release rate per unit floor area and growth times for a number of fuel arrays.[12] The values in the Fire Dynamics Tools for pallets, cartons and plastics are of this kind.[25] Such data describe free burning in the open. A pool in a room that receives significant radiation from a hot layer can burn faster, and no simple formula exists for that increase.[26]

Use in design fires and fire models

In a design fire, the heat release rate per unit area converts a heat release rate curve into a fire area. The OZone method first builds the heat release rate curve and then derives the fire area by dividing it by the effective heat release rate per unit area. The maximum heat release rate is reached when the whole floor area carrying fuel is burning.[3][16] At flashover the OZone model jumps directly to this maximum, the full fire area times the heat release rate per unit area.[27]

The area matters for several calculations. Plume entrainment and flame height correlations need the diameter of the fire, which follows from the area.[15][9] In CFD models, the fire is modelled as a burning surface. C/VM2 (second edition, 2025) states that its plan area follows from the peak heat release rate per unit area, and gives a range to suit different heat release rates and mesh sizes.[8] The Fire Dynamics Simulator converts a specified heat release rate per unit area, a time ramp and a heat of combustion into a mass flux of fuel from the burning surface.[4]

A t-squared fire can be interpreted with the same quantity. The Fire Dynamics Tools describe it as a fire in which the heat release rate per unit area is constant and the burning area spreads as a circle with a steadily growing radius.[28] The 2013 commentary on C/VM2 uses the same picture of a constant flame speed.[29] Heskestad applied it to a storage fire with a growth time of 140 s and 2,270 kW/m2, which gave a fire diameter growing in proportion to time.[30]

The heat release rate per unit area also links power to the duration of burning. The Fire Dynamics Tools estimate the burning duration of a solid fuel as its mass times its heat of combustion, divided by the heat release rate per unit area times the exposed area.[10] Energy per unit area is the fire load density, so dividing it by the heat release rate per unit area gives a first estimate of how long each square metre can burn. For an office FLED of 800 MJ/m2 and 250 kW/m2, the result is 3,200 s, or about 53 minutes.[31][8] In the gasoline spill example, the whole spill would burn away in about 2 minutes, which Gottuk and White consider most likely too short, because flames take time to spread across the spill.[17]

Limits and common misconceptions

The assumption of a constant heat release rate per unit area is a simplification. The OZone authors call it quite crude, particularly in the early stages of a fire, although they expect a small influence on the overall design.[16] In real fires, the rate per unit area changes as items ignite, burn at their peak and burn out, so a single value describes an average.[16][24]

A common misconception is to confuse the heat release rate per unit area with heat flux. Heat flux is the heat arriving at a surface, such as the radiation from the cone heater onto a test specimen. The heat release rate per unit area is the heat produced by the burning fuel itself. The technical guide of the Fire Dynamics Simulator keeps them apart. It treats a cone heat flux of 50 kW/m2 and the flame heat flux separately from prescribed values of 100 to 2,000 kW/m2 for the heat release rate per unit area.[32] Both quantities use the same unit, kW/m2, which adds to the confusion.[23]

Another misconception is that a value per unit area is a fixed material property. It depends on the scale of the test, the arrangement of the fuel, the incident heat flux and, for liquids, the depth of the pool.[24][22] Values per unit floor area of stacked fuels also depend on stack height.[7] Data must therefore be taken from tests that resemble the situation being modelled.

The choice of value also changes model results without changing the heat release rate. A higher value gives a smaller, more concentrated fire, while a lower value spreads the same power over a larger area.[1] This is why C/VM2 gives a range for CFD models rather than a single value, and why Introduction to Fire Safety Engineering recommends variant calculations with higher values for early-phase modelling.[8][21]

See also

Notes

  1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Van Rossum (2027), §4.6.
  2. ↑ 2.0 2.1 Cadorin and Franssen (2003), p. 417.
  3. ↑ 3.0 3.1 3.2 3.3 3.4 Cadorin et al. (2003), p. 435.
  4. ↑ 4.0 4.1 McGrattan et al. (2026), p. 82.
  5. ↑ Van Rossum (2027), §4.5.
  6. ↑ Iqbal and Salley (2004), p. 2-20.
  7. ↑ 7.0 7.1 7.2 7.3 Iqbal and Salley (2004), p. 2-22.
  8. ↑ 8.0 8.1 8.2 8.3 8.4 Ministry of Business, Innovation and Employment (2025b), p. 20.
  9. ↑ 9.0 9.1 9.2 Heskestad (2002), p. 2-3.
  10. ↑ 10.0 10.1 10.2 Iqbal and Salley (2004), p. 8-2.
  11. ↑ Babrauskas (2002b), p. 3-24.
  12. ↑ 12.0 12.1 Heskestad (2002), p. 2-15.
  13. ↑ 13.0 13.1 13.2 Walton and Thomas (2002), p. 3-173.
  14. ↑ 14.0 14.1 Gottuk and White (2002), p. 2-312.
  15. ↑ 15.0 15.1 Cadorin and Franssen (2003), p. 418.
  16. ↑ 16.0 16.1 16.2 16.3 Cadorin et al. (2003), p. 436.
  17. ↑ 17.0 17.1 17.2 Gottuk and White (2002), p. 2-314.
  18. ↑ Iqbal and Salley (2004), p. 2-19.
  19. ↑ Iqbal and Salley (2004), p. 2-21.
  20. ↑ Heskestad (2002), p. 2-11.
  21. ↑ 21.0 21.1 21.2 Van Rossum (2027), §8.5.
  22. ↑ 22.0 22.1 Babrauskas (2002b), p. 3-25.
  23. ↑ 23.0 23.1 23.2 Babrauskas (2002a), p. 3-63.
  24. ↑ 24.0 24.1 24.2 24.3 Babrauskas (2002a), p. 3-70.
  25. ↑ Iqbal and Salley (2004), p. 8-3.
  26. ↑ Babrauskas (2002b), p. 3-26.
  27. ↑ Cadorin et al. (2003), p. 438.
  28. ↑ Iqbal and Salley (2004), p. B-4.
  29. ↑ Ministry of Business, Innovation and Employment (2013), p. 55.
  30. ↑ Heskestad (2002), p. 2-13.
  31. ↑ Ministry of Business, Innovation and Employment (2025b), p. 22.
  32. ↑ McGrattan et al. (2026), p. 228.

References

  • 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.
  • Cadorin, J.-F., & Franssen, J.-M. (2003). A tool to design steel elements submitted to compartment fires – OZone V2. Part 1: Pre- and post-flashover compartment fire model. Fire Safety Journal, 38, 395–427. https://doi.org/10.1016/S0379-7112(03)00014-6
  • Cadorin, J.-F., Pintea, D., Dotreppe, J.-C., & Franssen, J.-M. (2003). A tool to design steel elements submitted to compartment fires – OZone V2. Part 2: Methodology and application. Fire Safety Journal, 38, 429–451. https://doi.org/10.1016/S0379-7112(03)00015-8
  • Gottuk, D. T., & White, D. A. (2002). Liquid fuel 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. 2-297–2-316). National Fire Protection Association; Society of Fire Protection Engineers.
  • Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. 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. 2-1–2-17). 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.
  • McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). Fire Dynamics Simulator technical reference guide: Vol. 1. Mathematical model (6th ed., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
  • 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.).
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
  • Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment 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. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.
Retrieved from "https://fire-safety.academy/w/index.php?title=Heat_release_rate_per_unit_area&oldid=326"