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Radiative fraction

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Contents
  1. 1Defining the energy division
  2. 2Different quantities that can be confused
  3. 3Fuel, soot and scale
  4. 4Values in simplified models
  5. 5Worked energy divisions
  6. 6Local fractions in field modelling
  7. 7Interpreting uncertainty
  8. 8Notes
  9. 9References

Radiative fraction is the proportion of a fire's actual heat release that leaves the source as thermal radiation. It relates the total radiative power to the total heat release rate. The remaining released energy is commonly represented as heat carried by the moving gases. This division connects the source fire to both radiation exposure and plume calculations.[1][2]

The fraction depends on fuel, burning conditions, fire size and the boundary at which radiation is counted. It is not the same quantity as emissivity or combustion efficiency. A nominal fraction assigned to a flaming region may also differ from the fraction escaping a larger surrounding smoke envelope.[3][4] Values used in different engineering methods therefore need their original definitions and assumptions. A default value in a computer model is a modelling choice, rather than a measured property shared by all fires.[3]

Defining the energy division

A fire releases chemical energy through combustion. Some of that energy is emitted as electromagnetic radiation, while another part heats gases carried away from the source. The radiative fraction expresses the first contribution relative to the actual released power. It describes an energy division at the source, before any particular target's geometry is considered.[1][2]

Fire power splits into radiation and convection before geometry determines the radiation reaching a target.
The source energy division precedes calculation of radiation received by a target. Based on Heskestad (2002), chapter 2-1, p. 2-2, Peacock et al. (2026), p. 12, and Beyler (2002), chapter 3-11, p. 3-274.

In the two part representation used by the supplied CFAST technical reference, the radiative power is the selected fraction multiplied by total heat release. The convective power is the complementary fraction multiplied by that same total. These expressions use a consistent definition of actual heat release, already accounting for combustion efficiency.[3]

χr = Q̇r/Q̇
Q̇r = χr Q̇
Q̇c = (1 − χr) Q̇
Symbol Description Unit
χr Radiative fraction for the stated source boundary dimensionless
Q̇ Actual total heat release rate kW
Q̇r Radiative power kW
Q̇c Convective power in the stated division kW

These quantities are powers, rather than energies accumulated over the entire fire. A constant fraction applied to a changing heat release produces radiative power that changes with the fire. The fraction itself can also depend on the burning conditions represented. Assuming that it remains constant is an additional simplification, separate from prescribing the heat release history.[3]

The definition also requires a consistent boundary around the source. Radiation emitted inside a flame can subsequently be absorbed by surrounding combustion products. A measurement farther away may therefore count less outgoing radiation than was initially emitted within the reacting region. The model's local and global definitions must be distinguished before comparing their fractions.[4]

Different quantities that can be confused

Combustion efficiency concerns how much of the fuel's theoretical energy is actually released. Radiative fraction concerns how the released energy is divided. The two quantities therefore have different denominators and different roles. Applying a radiative fraction to theoretical power without accounting for the intended combustion efficiency can produce an inconsistent source description.[1][3]

Emissivity is also a different quantity. It relates emission from a material or gas body to blackbody emission at the same temperature, within the stated spectral and geometric assumptions. Radiative fraction instead relates emitted power to combustion power. A large emissivity does not by itself specify the fraction of chemical heat that escapes the fire as radiation.[5][2]

Soot yield expresses the mass of soot produced relative to the consumed fuel mass. It can influence radiation because soot particles emit and absorb, but its numerical value is not a radiative fraction. The two inputs describe different physical processes. Substituting a soot mass percentage for an energy fraction would therefore confuse species production with heat transfer.[6][5]

The radiant heat flux received by an object is another separate result. It depends on how radiative power is distributed through space and intercepted by the target. Distance, orientation and intervening absorption can change the exposure while the source fraction remains unchanged. Source emission and target receipt consequently occupy different stages of a radiation assessment.[7]

These distinctions matter when comparing tables from different sources. A column containing emissive power per square metre cannot be used directly as a dimensionless fraction. Similarly, a radiative fraction inferred through one assumed flame geometry carries that interpretation. The reported quantity and its calculation method both need to accompany its numerical value.[2][8]

Fuel, soot and scale

Flame radiation arises from hot gases and suspended particles. Water vapour and carbon dioxide contribute through their radiative properties, while soot can make a substantial contribution. The amount of soot, its temperature and the paths through the radiating volume affect the energy that escapes. A simple association between visible brightness and a single fixed fraction therefore omits part of the process.[5][9]

Fuel differences are reflected in the ranges reported by engineering sources. NUREG-1805 gives approximate values from 0.15 for low sooting fuels to 0.60 for high sooting fuels in its discussion of point source radiation. The report also states that fuel, flame size and configuration influence the fraction. Those values belong to that discussion, rather than establishing a universal interval for every fire model.[10]

Increasing fire size can change the relationship between emission and escape. Cooler soot surrounding luminous flames can absorb radiation emitted farther inside the fire. NUREG-1805 identifies this effect for large fires, and the supplied Fire Dynamics Simulator reference distinguishes local emission from global radiation leaving the smoke mantle. More soot can therefore increase emission locally while also increasing absorption along an outgoing path.[10][4]

Some radiation from a flame is absorbed in surrounding smoke before it reaches the outer boundary.
Radiation emitted in a flame can be absorbed before leaving the surrounding smoke mantle. Based on McGrattan et al. (2026), pp. 66–69, and Iqbal and Salley (2004), p. 5-3.

The spectral properties of the participating material also matter. Combustion gases emit and absorb strongly in particular wavelength bands, whereas soot has a more continuous spectrum. The supplied Fire Dynamics Simulator reference uses this distinction to explain its grey gas approximation and alternatives for low soot flames. A radiative fraction summarises an energy outcome without resolving those spectral details by itself.[11]

Ventilation and combustion conditions introduce further variation. The CFAST technical reference identifies vitiation, fuel type, scale and combustion efficiency as influences on radiative output. A value measured for one burning regime may therefore be unsuitable for another. The source notes uncertainty associated with retaining constant fractions throughout a calculation.[3]

Values in simplified models

Van Rossum describes a commonly assumed division of 30% radiation and 70% convection in a two zone fire calculation. The convective portion is used to describe energy transported towards the smoke layer. The text also states that this division is no longer realistic in the post-flashover phase. The percentage is consequently a contextual approximation, not an unrestricted property of fire.[12]

The supplied CFAST Version 7 technical reference, revised in May 2026, specifies a default radiative fraction of 0.35. It describes a typical range of about 0.05–0.4 and emphasises scenario dependence. Its default and range are part of that documented modelling treatment. They need not match a range quoted for a different class of fires or a different definition of emitted radiation.[3]

A point source model can use radiative fraction to turn total fire power into an equivalent radiating source. Beyler's particular pool fire method uses a fraction fitted as a function of pool diameter. The values were inferred from experimental radiation measurements using the same point source representation. They therefore include the interpretation imposed by that method.[2]

For that pool fire procedure, the relationship is χr = 0.21 − 0.0034D, with diameter D in metres. The source specifies that the value at 50 m is retained for larger diameters. This limit prevents unrestricted continuation of the fitted trend. The expression is not a general fuel property relation for all fire geometries.[2]

Method consistency matters because radiative properties and geometric assumptions are calibrated together. Beyler explicitly cautions against combining selected components from unrelated pool fire methodologies. A fraction fitted through a point representation cannot automatically be transferred to a solid flame surface calculation. Such a transfer would require a consistent account of the emitting area and radiation distribution.[13]

The experimental interpretation in Beyler's procedure uses the most remote measurement point from each fire test. A fraction is inferred through the assumed point source geometry and then fitted against pool diameter. This construction differs from measuring every direction of emission around the entire fire. The inferred fraction is therefore inseparable from the representation used to interpret the detector reading.[2]

The distinction also explains why an effective radiative fraction can be useful without being an intrinsic material constant. It provides an input that reproduces a class of observations within a specified method. Transfer to another source shape or a strongly different observation distance requires evidence beyond the fitted number itself. The chapter's instruction to retain a consistent methodology addresses that dependence.[13][2]

Worked energy divisions

Consider a prescribed fire power of 1 MW, matching the power used in Van Rossum's illustrative smoke calculation. Applying the supplied CFAST default fraction of 0.35 produces 350 kW of radiative power. The complementary convective power is 650 kW. This is an arithmetic illustration of the defined division, rather than a measurement of a particular fuel mixture.[14][3]

Using Van Rossum's contextual fraction of 0.30 instead gives 300 kW of radiation and 700 kW of convection for the same total power. The total remains unchanged, but the inputs to radiation and plume calculations differ. This comparison demonstrates why changing the fraction affects more than one part of a fire model. It does not establish which choice is correct for an unspecified scenario.[12][3]

Equal 1 MW bars compare 300/700 kW and 350/650 kW radiation/convection divisions.
Different assumed fractions redistribute the same prescribed fire power. Based on Van Rossum (2027), §§6.5 and 9.3, and Peacock et al. (2026), p. 12.

The range quoted in the CFAST reference gives another sensitivity illustration. Fractions of 0.05 and 0.40 produce radiative powers of 50 kW and 400 kW respectively at the same 1 MW total. Their complementary convective powers are 950 kW and 600 kW. These endpoints show the possible importance of the input without assigning probabilities to values within the range.[3]

Beyler's separate toluene pool example illustrates a method dependent fraction. The pool diameter is 12 m, so the fitted expression gives 0.1692, or about 0.169. The stated burning rate and heat of combustion give a total power of approximately 516 MW. Multiplying by the fitted fraction gives about 87.4 MW of radiative power.[15]

This pool result differs from applying a generic fraction of 0.30 or 0.35. The difference follows from using a particular calibrated pool fire procedure. It should not be interpreted as a contradiction that can be resolved by averaging the fractions. Each value belongs to a source definition, physical regime and method that must remain explicit.[13][2][3]

Local fractions in field modelling

The supplied Fire Dynamics Simulator technical reference treats radiation as transport through emitting and absorbing gases and particles. It distinguishes the energy emitted within a calculation cell from the energy absorbed there. The net radiative contribution to the gas energy balance is the difference between those terms. Radiation can therefore move energy within the fire environment before finally reaching a boundary.[11]

The same reference explains why computed cell temperatures cannot always be inserted directly into a flame emission calculation. Cells represent average conditions over a finite volume, while real flame temperatures vary at smaller scales. Emission depends strongly on absolute temperature. The method therefore corrects the emission source in the flaming region to obtain a specified nominal radiative fraction.[16]

In that formulation, the fraction refers to radiation emitted from the flaming region. For a small fire, its local and global values can be approximately equal. As the fire becomes larger, absorption by the increasing smoke mantle can reduce the global fraction. The technical reference explicitly separates these meanings when explaining the model input.[4]

Different fuels can also have different reaction specific fractions in the documented formulation. Their contributions are combined using the local reaction rates. This approach retains more information than assigning one universal value to every reacting material. It still depends on the supplied values and the combustion representation used in the calculation.[4]

Interpreting uncertainty

A selected fraction does not determine the full thermal radiation field. The receiving geometry, intervening material and source representation remain necessary. The same emitted power can produce different local fluxes at different positions. Uncertainty in those elements must therefore be considered separately from uncertainty in the energy fraction.[7]

A reported range also does not automatically describe the probability distribution of a chosen fire. The CFAST, NUREG and Fire Dynamics Simulator discussions concern different modelling contexts and boundaries. Their values can illustrate sensitivity, but cannot simply be pooled as interchangeable measurements. The calculation's definition of radiative output is needed before a meaningful comparison can be made.[3][10][4]

Finally, an assumed constant fraction can conceal changes during fire development. Fuel composition, scale and oxygen availability may evolve while the prescribed heat release changes. The supplied sources identify these influences but do not supply a universal time dependent correction. A model using one value consequently retains that simplification as part of its uncertainty.[3][12]

Notes

  1. ↑ 1.0 1.1 1.2 Heskestad (2002), chapter 2-1, p. 2-2.
  2. ↑ 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Beyler (2002), chapter 3-11, p. 3-274.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 Peacock et al. (2026), p. 12.
  4. ↑ 4.0 4.1 4.2 4.3 4.4 4.5 McGrattan et al. (2026), p. 69.
  5. ↑ 5.0 5.1 5.2 Tien, Lee, and Stretton (2002), chapter 1-4, pp. 1-73–1-75.
  6. ↑ Van Rossum (2027), §6.2.
  7. ↑ 7.0 7.1 Beyler (2002), chapter 3-11, pp. 3-269–3-274.
  8. ↑ Iqbal and Salley (2004), pp. 5-6–5-7.
  9. ↑ Tien, Lee, and Stretton (2002), chapter 1-4, pp. 1-78–1-79.
  10. ↑ 10.0 10.1 10.2 Iqbal and Salley (2004), p. 5-3.
  11. ↑ 11.0 11.1 McGrattan et al. (2026), pp. 65–66.
  12. ↑ 12.0 12.1 12.2 Van Rossum (2027), §9.3.
  13. ↑ 13.0 13.1 13.2 Beyler (2002), chapter 3-11, p. 3-272.
  14. ↑ Van Rossum (2027), §6.5.
  15. ↑ Beyler (2002), chapter 3-11, p. 3-286.
  16. ↑ McGrattan et al. (2026), pp. 66–69.

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.
  • Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. In P. J. DiNenno (Ed.), SFPE handbook of fire protection engineering (3rd ed., pp. 2-1–2-17). 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.
  • Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). CFAST: Consolidated fire and smoke transport (version 7). Volume 1: Technical reference guide (revision CFAST-7.7.7; NIST TN 1889v1). 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.
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