Adiabatic flame temperature - Revision history

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	Beyler reports the same pattern for a wide range of fuels that contain only carbon, hydrogen and oxygen: about 1,600 K, with a spread of ±150 K.<ref name="BE-177" /> Hydrogen at 980 K, carbon monoxide at 1,300 K and acetylene at 1,280 K are notable exceptions. A lower limiting temperature indicates a more reactive fuel.<ref name="BE-177" /> Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.<ref name="BE-177" />		Beyler reports the same pattern for a wide range of fuels that contain only carbon, hydrogen and oxygen: about 1,600 K, with a spread of ±150 K.<ref name="BE-177" /> Hydrogen at 980 K, carbon monoxide at 1,300 K and acetylene at 1,280 K are notable exceptions. A lower limiting temperature indicates a more reactive fuel.<ref name="BE-177" /> Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.<ref name="BE-177" />
	[[File:fse-adiabatic-flame-temperature-v3.svg\|thumb\|upright=1.5\|alt=Bar chart of seven alkanes~~; all~~ lower-limit flame temperatures ~~lie between~~ 1,446 ~~and~~ 1,692 K~~, inside a~~ band of 1,500 to 1,700 K.\|Adiabatic flame temperature of seven hydrocarbon and air mixtures at the lower flammability limit, with the band of 1,600 ± 100 K. Based on Drysdale (2002), p. 1-97.]]		[[File:fse-adiabatic-flame-temperature-v3.svg\|thumb\|upright=1.5\|alt=Bar chart of seven alkanes with lower-limit flame temperatures from 1,446 to 1,692 K. The shaded reference band spans 1,500 to 1,700 K.\|Adiabatic flame temperature of seven hydrocarbon and air mixtures at the lower flammability limit, with the band of 1,600 ± 100 K. Based on Drysdale (2002), p. 1-97.]]

	== Limiting flame temperature ==		== Limiting flame temperature ==

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	== Calculation ==		== Calculation ==
	The adiabatic flame temperature follows from an energy balance. The heat released by the reaction at the initial temperature of the reactants must equal the heat needed to raise the combustion products from that initial temperature to the final flame temperature.<ref name="SI-145" /> In equation form this balance reads:		The adiabatic flame temperature follows from an energy balance. The heat released by the reaction at the initial temperature of the reactants must equal the heat needed to raise the combustion products from that initial temperature to the final flame temperature.<ref name="SI-145" /> In equation form this balance reads:
			[[File:fse-adiabatic-flame-temperature-v1.svg\|thumb\|upright=1.5\|alt=Two energy-balance sketches: left, all reaction heat stays in the products; right, part of it leaves the flame as radiation.\|The adiabatic flame temperature assumes that all heat released by the reaction warms the products (left). A real flame loses heat by radiation and dissociation, so it stays cooler (right). Based on Simmons (2002), p. 1-145 and Drysdale (2002), p. 1-96.]]

	<math display="block">\Delta H_r^0 = \int_{T_i}^{T_f} C_p \, \mathrm{d}T</math>		<math display="block">\Delta H_r^0 = \int_{T_i}^{T_f} C_p \, \mathrm{d}T</math>
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	In rooms, the peak temperature is governed by the ventilation and the fuel supply. The maximum is around 1,200 °C, while a typical fire after flashover more commonly peaks at 900 to 1,000 °C.<ref name="IS-314" /> Heat loss from the flame determines how far the actual temperature stays below the adiabatic flame temperature. A flame far from any wall radiates to surroundings at about 20 °C. In a small room, or near a large fire, the walls heat up to several hundred degrees Celsius, so the radiation losses fall and the flame becomes hotter.<ref name="IS-314" />		In rooms, the peak temperature is governed by the ventilation and the fuel supply. The maximum is around 1,200 °C, while a typical fire after flashover more commonly peaks at 900 to 1,000 °C.<ref name="IS-314" /> Heat loss from the flame determines how far the actual temperature stays below the adiabatic flame temperature. A flame far from any wall radiates to surroundings at about 20 °C. In a small room, or near a large fire, the walls heat up to several hundred degrees Celsius, so the radiation losses fall and the flame becomes hotter.<ref name="IS-314" />
			[[File:fse-adiabatic-flame-temperature-v2.svg\|thumb\|upright=1.5\|alt=Bar chart: calculated flame temperatures of 1,600 to 2,467 K compared with measured fire temperatures of about 600 to 1,470 K.\|Calculated adiabatic flame temperatures (top) compared with measured temperatures in fires (bottom). Based on Drysdale (2002), p. 1-96 and Iqbal and Salley (2004), pp. 3-14 and B-25.]]

	Laboratory premixed flames come much closer to the adiabatic value.<ref name="SI-144" /> In a burner flame of 7.5 % natural gas in air, the highest measured temperature contour lies at 1,755 °C.<ref name="SI-145" /> Such a flame burns a mixture that was fully mixed before ignition, as in a gas burner. The flame in a real fire, by contrast, is essentially a diffusion flame, in which oxygen reaches the fuel by diffusion or turbulence.<ref name="VR-4.3" /><ref name="SI-147" />		Laboratory premixed flames come much closer to the adiabatic value.<ref name="SI-144" /> In a burner flame of 7.5 % natural gas in air, the highest measured temperature contour lies at 1,755 °C.<ref name="SI-145" /> Such a flame burns a mixture that was fully mixed before ignition, as in a gas burner. The flame in a real fire, by contrast, is essentially a diffusion flame, in which oxygen reaches the fuel by diffusion or turbulence.<ref name="VR-4.3" /><ref name="SI-147" />
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	Beyler reports the same pattern for a wide range of fuels that contain only carbon, hydrogen and oxygen: about 1,600 K, with a spread of ±150 K.<ref name="BE-177" /> Hydrogen at 980 K, carbon monoxide at 1,300 K and acetylene at 1,280 K are notable exceptions. A lower limiting temperature indicates a more reactive fuel.<ref name="BE-177" /> Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.<ref name="BE-177" />		Beyler reports the same pattern for a wide range of fuels that contain only carbon, hydrogen and oxygen: about 1,600 K, with a spread of ±150 K.<ref name="BE-177" /> Hydrogen at 980 K, carbon monoxide at 1,300 K and acetylene at 1,280 K are notable exceptions. A lower limiting temperature indicates a more reactive fuel.<ref name="BE-177" /> Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.<ref name="BE-177" />
			[[File:fse-adiabatic-flame-temperature-v3.svg\|thumb\|upright=1.5\|alt=Bar chart of seven alkanes; all lower-limit flame temperatures lie between 1,446 and 1,692 K, inside a band of 1,500 to 1,700 K.\|Adiabatic flame temperature of seven hydrocarbon and air mixtures at the lower flammability limit, with the band of 1,600 ± 100 K. Based on Drysdale (2002), p. 1-97.]]

	== Limiting flame temperature ==		== Limiting flame temperature ==
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	At an initial temperature of 200 °C (473 K), the same ratio gives a limit fraction of (1,600 − 473)/(6.22 × 10<sup>4</sup>) = 0.0181. The lower flammability limit of propane therefore falls to 1.8 %.<ref name="BE-178" /> Flammability limits generally widen as the temperature of a mixture increases.<ref name="SI-147" /> Beyler extends the method to mixtures of fuels, and the approach has been used to predict whether the hot gas layer of an enclosure fire can ignite.<ref name="BE-184" />		At an initial temperature of 200 °C (473 K), the same ratio gives a limit fraction of (1,600 − 473)/(6.22 × 10<sup>4</sup>) = 0.0181. The lower flammability limit of propane therefore falls to 1.8 %.<ref name="BE-178" /> Flammability limits generally widen as the temperature of a mixture increases.<ref name="SI-147" /> Beyler extends the method to mixtures of fuels, and the approach has been used to predict whether the hot gas layer of an enclosure fire can ignite.<ref name="BE-184" />
			[[File:fse-adiabatic-flame-temperature-v4.svg\|thumb\|upright=1.5\|alt=Line chart: the lower flammability limit of propane falls from 2.13 % at 0 °C to 1.65 % at 300 °C.\|Lower flammability limit of propane predicted from a limiting flame temperature of 1,600 K, for initial temperatures of 0 to 300 °C. Based on Beyler (2002b), p. 2-178.]]

	In a closed vessel, the temperature rise of a burning mixture causes a matching rise in pressure. NUREG-1805 estimates the maximum pressure from the ratio of absolute temperatures:<ref name="IS-1514">Iqbal and Salley (2004), p. 15-14.</ref>		In a closed vessel, the temperature rise of a burning mixture causes a matching rise in pressure. NUREG-1805 estimates the maximum pressure from the ratio of absolute temperatures:<ref name="IS-1514">Iqbal and Salley (2004), p. 15-14.</ref>

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Mark: New FSE wiki article: Adiabatic flame temperature (written by Claude Opus 5.5)

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New FSE wiki article: Adiabatic flame temperature (written by Claude Opus 5.5)

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'''Adiabatic flame temperature''' is the highest temperature that the products of a combustion reaction can reach when none of the released heat is lost to the surroundings.<ref name="DR-96">Drysdale (2002), p. 1-96.</ref><ref name="IS-315">Iqbal and Salley (2004), p. 3-15.</ref> It is a calculated value, found from an energy balance between the [[heat of combustion]] of the fuel and the heat needed to warm the products, any excess reactants and inert gases such as nitrogen.<ref name="DR-96" /> A real [[flame]] always loses heat, so its temperature stays below this ideal value.<ref name="IS-314">Iqbal and Salley (2004), p. 3-14.</ref> For most flammable gases burning in air in exactly the right proportions, the adiabatic flame temperature is about 2,300 K. Mixtures at the [[Flammability limits|lower flammability limit]] reach only about 1,600 K.<ref name="IS-B25">Iqbal and Salley (2004), p. B-25.</ref>

The second value explains why the concept matters in fire safety engineering. Many fuel mixtures cannot sustain a flame once their adiabatic flame temperature falls below a limiting value of roughly 1,600 K.<ref name="BE-177">Beyler (2002), p. 2-177.</ref><ref name="DR-97">Drysdale (2002), p. 1-97.</ref> Engineers use this limiting value to predict flammability limits, the effect of inert gases and water mist, and the risk that a hot gas layer will ignite.<ref name="MB-313">Mawhinney and Back (2002), p. 4-313.</ref><ref name="BE-184">Beyler (2002), p. 2-184.</ref> The adiabatic flame temperature also sets an upper bound for checking calculated gas temperatures, explosion pressures and radiant heat fluxes.<ref name="CK-206">Cox and Kumar (2002), p. 3-206.</ref><ref name="BA-6">Babrauskas (2002), p. 3-6.</ref>

== Definition and physical meaning ==
Combustion is a set of mainly exothermic chemical reactions between a fuel and an oxidiser, usually oxygen, which produces heat and light in the form of a flame or a glow.<ref name="VR-4.1">Van Rossum (2027), §4.1.</ref> The released energy is first absorbed within the reacting system itself. Unreacted reactants, combustion products and diluents such as nitrogen all take up part of it, before the heat is finally lost by heat transfer.<ref name="DR-96" /> The word adiabatic means that no heat is transferred to or from the system. If a premixed system, such as a flammable vapour mixed with air, is assumed to be adiabatic, the maximum theoretical temperature of its products can be calculated. That temperature is the adiabatic flame temperature.<ref name="DR-96" />

The concept is closely tied to [[stoichiometry]], which describes the proportions in which substances are consumed and formed in a chemical reaction.<ref name="VR-3.3">Van Rossum (2027), §3.3.</ref> A stoichiometric mixture contains exactly enough oxygen to burn all of the fuel. The further a mixture departs from this ratio, the slower the combustion, because substances that do not take part in the reaction are still heated by it.<ref name="VR-3.3" /> The same reasoning explains the role of the oxidiser. In air, part of the heat of combustion is spent on heating nitrogen, which contributes nothing to the energy release. A given fuel therefore always has a higher adiabatic flame temperature in pure oxygen than in normal air with 21 % oxygen.<ref name="IS-315" />

No real system is free of heat loss, so the adiabatic flame temperature is never reached in a fire. It is always a calculated value rather than a measured one.<ref name="IS-315" /> In a sufficiently large premixed flame, the calculated value is nearly reached in the middle of the gas stream, just above the inner cone of the flame.<ref name="SI-144">Simmons (2002), p. 1-144.</ref> Small premixed flames and turbulent flames of all kinds normally fall short of it, because their heat losses are appreciable.<ref name="SI-145">Simmons (2002), p. 1-145.</ref>

== Calculation ==
The adiabatic flame temperature follows from an energy balance. The heat released by the reaction at the initial temperature of the reactants must equal the heat needed to raise the combustion products from that initial temperature to the final flame temperature.<ref name="SI-145" /> In equation form this balance reads:

<math display="block">\Delta H_r^0 = \int_{T_i}^{T_f} C_p \, \mathrm{d}T</math>

The heat capacity in this integral covers all of the product gases, including excess oxygen and nitrogen.<ref name="DR-96" /> The calculation neglects every heat loss from the flame, whether by radiation, by conduction or by diffusion to a wall.<ref name="SI-145" /> The [[specific heat capacity]] of a substance is the heat needed to raise a unit mass by one kelvin. For gases it matters whether the heating takes place at constant pressure or at constant volume, and for air and smoke the constant-pressure value is about 40 % larger. A fire is usually an open system in which the gases can expand, so the constant-pressure value is used.<ref name="VR-3.4">Van Rossum (2027), §3.4.</ref>

When an average heat capacity is taken for each product gas over the temperature range of interest, the integral reduces to a division. The heat of combustion per mole of fuel is divided by the total heat capacity of the products formed from one mole of fuel:<ref name="DR-96" />

<math display="block">\Delta T = T_f - T_i = \frac{\Delta H_c}{\sum_j n_j \, C_{p,j}}</math>

{| class="wikitable"
|+ Symbols used in the energy balance
! Symbol !! Description !! Unit
|-
| <math>\Delta H_r^0</math> || heat released by the reaction at the initial temperature, per mole of fuel || J/mol
|-
| <math>\Delta H_c</math> || heat of combustion per mole of fuel || J/mol
|-
| <math>T_i</math> || initial temperature of the reactants || K
|-
| <math>T_f</math> || final (adiabatic) flame temperature || K
|-
| <math>\Delta T</math> || temperature rise of the products || K
|-
| <math>C_p</math> || heat capacity of the products at constant pressure, per mole of fuel || J/(mol·K)
|-
| <math>n_j</math> || number of moles of product gas ''j'' formed per mole of fuel || –
|-
| <math>C_{p,j}</math> || average molar heat capacity of product gas ''j'' || J/(mol·K)
|}

=== Worked example: propane in air ===
Drysdale illustrates the method with a stoichiometric mixture of propane and air that is initially at 25 °C.<ref name="DR-96" /> The overall reaction is:

<math display="block">\mathrm{C_3H_8} + 5\,\mathrm{O_2} + 18.8\,\mathrm{N_2} \rightarrow 3\,\mathrm{CO_2} + 4\,\mathrm{H_2O} + 18.8\,\mathrm{N_2}</math>

This reaction releases 2,044 kJ for every mole of propane consumed. The energy heats 3 moles of carbon dioxide, 4 moles of water vapour and 18.8 moles of nitrogen. With average heat capacities at 1,000 K, these products have a total heat capacity of 942.5 J/K per mole of propane.<ref name="DR-96" /> The temperature rise then follows directly from the division:

<math display="block">\Delta T = \frac{2.044 \times 10^{6}\ \mathrm{J}}{942.5\ \mathrm{J/K}} \approx 2169\ \mathrm{K}</math>

{| class="wikitable"
|+ Heat capacity of the products per mole of propane, at 1,000 K<ref name="DR-96" />
! Product !! Moles !! Molar heat capacity (J/(mol·K)) !! Heat capacity (J/K)
|-
| Carbon dioxide || 3 || 54.3 || 162.9
|-
| Water vapour || 4 || 41.2 || 164.8
|-
| Nitrogen || 18.8 || 32.7 || 614.8
|-
| Total || || || 942.5
|}

Adding the initial temperature of 298 K gives an adiabatic flame temperature of 2,467 K.<ref name="DR-96" /> Drysdale stresses that this result is approximate, for three reasons. Heat capacities change with temperature, the hot carbon dioxide and water vapour lose heat by radiation, and at high temperatures the products dissociate in reactions that absorb heat. Once these effects are included, propane burning in air may not exceed 2,000 K.<ref name="DR-96" />

The same reaction in pure oxygen shows the role of nitrogen as a heat sink. Without the 18.8 moles of nitrogen, the heat capacity of the products falls to 327.7 J/K. The simple calculation then predicts a temperature rise of 6,238 K. Dissociation dominates at such temperatures, so the flame in fact stays below about 3,500 K.<ref name="DR-96" />

=== Equilibrium calculations ===
Above about 1,800 K, the heat taken up by the dissociation of carbon dioxide, steam and oxygen must be included in the balance.<ref name="SI-145" /> The product composition then depends on the temperature, while the temperature depends on the composition. The solution requires successive approximations, which are most conveniently carried out with a computer program.<ref name="SI-146">Simmons (2002), p. 1-146.</ref> Chemical equilibrium programs such as STANJAN can calculate the adiabatic flame temperature of a specific mixture, for example the contents of a particular tank.<ref name="IS-B25" /> For lean mixtures with relatively low flame temperatures, the products follow directly from the overall stoichiometry, and the simple method is adequate.<ref name="SI-145" />

== Real flame temperatures ==
Measured flame temperatures in fires lie far below the adiabatic values.<ref name="IS-314" /> McCaffrey studied turbulent diffusion flames above gas burners and found temperatures slightly below 900 °C in the continuous flame region. At the visible flame tips, the temperature had fallen to about 320 °C.<ref name="McC">McCaffrey (1979), as cited in Iqbal and Salley (2004), p. 3-14.</ref> For flames smaller than about 1 m across, continuous flame temperatures of around 900 °C should be expected. For large pool fires this value can rise to 1,100 to 1,200 °C.<ref name="IS-314" /> In a candle flame, which is a laminar diffusion flame, the outer zone is the hottest part and reaches about 1,400 °C.<ref name="VR-4.3">Van Rossum (2027), §4.3.</ref>

In rooms, the peak temperature is governed by the ventilation and the fuel supply. The maximum is around 1,200 °C, while a typical fire after flashover more commonly peaks at 900 to 1,000 °C.<ref name="IS-314" /> Heat loss from the flame determines how far the actual temperature stays below the adiabatic flame temperature. A flame far from any wall radiates to surroundings at about 20 °C. In a small room, or near a large fire, the walls heat up to several hundred degrees Celsius, so the radiation losses fall and the flame becomes hotter.<ref name="IS-314" />

Laboratory premixed flames come much closer to the adiabatic value.<ref name="SI-144" /> In a burner flame of 7.5 % natural gas in air, the highest measured temperature contour lies at 1,755 °C.<ref name="SI-145" /> Such a flame burns a mixture that was fully mixed before ignition, as in a gas burner. The flame in a real fire, by contrast, is essentially a diffusion flame, in which oxygen reaches the fuel by diffusion or turbulence.<ref name="VR-4.3" /><ref name="SI-147" />

== Typical values ==
For most flammable gases at atmospheric pressure, a stoichiometric mixture with air has an adiabatic flame temperature of about 2,300 K.<ref name="IS-B25" /> Simmons quotes about 2,200 K for a stoichiometric hydrocarbon and air mixture with an initial temperature of 300 K.<ref name="SI-147">Simmons (2002), p. 1-147.</ref> Babrauskas gives approximately 2,300 K for most organic fuels.<ref name="BA-6" /> Mixtures at the lower flammability limit are much cooler, because the excess air absorbs a large part of the heat. Drysdale calculates 1,554 K (1,281 °C) for propane at a lower limit of 2.2 %.<ref name="DR-96" /> For the other hydrocarbon gases, the limiting value lies in a narrow band of 1,600 ± 100 K.<ref name="DR-97">Drysdale (2002), p. 1-97.</ref>

{| class="wikitable"
|+ Adiabatic flame temperature of hydrocarbon and air mixtures at the lower flammability limit<ref name="DR-97" />
! Gas !! Adiabatic flame temperature (K)
|-
| Methane || 1,446
|-
| Ethane || 1,502
|-
| Propane || 1,554
|-
| n-Butane || 1,612
|-
| n-Pentane || 1,564
|-
| n-Heptane || 1,692
|-
| n-Octane || 1,632
|}

Beyler reports the same pattern for a wide range of fuels that contain only carbon, hydrogen and oxygen: about 1,600 K, with a spread of ±150 K.<ref name="BE-177" /> Hydrogen at 980 K, carbon monoxide at 1,300 K and acetylene at 1,280 K are notable exceptions. A lower limiting temperature indicates a more reactive fuel.<ref name="BE-177" /> Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.<ref name="BE-177" />

== Limiting flame temperature ==
The near-constant value at the lower limit has a physical explanation. A flame can only sustain itself while it produces heat faster than it loses heat, mainly by radiation. At the limit, the losses exceed the heat production and the flame can no longer propagate.<ref name="DR-97" /> As early as 1911, Burgess and Wheeler noted that lower-limit mixtures of alkanes in air release almost the same heat per unit volume. Since the products of all these fuels have nearly the same heat capacity, this observation implies a constant limiting flame temperature.<ref name="BW">Burgess and Wheeler (1911), as cited in Beyler (2002), p. 2-177.</ref> The limiting value is relatively insensitive, within about ±100 K, to the diluent used and to the initial temperature of the mixture.<ref name="BE-177" />

The same concept describes the effect of inert gases. Nitrogen, argon and carbon dioxide lower the final flame temperature, and if the burning velocity falls far enough, the flame goes out.<ref name="SI-150">Simmons (2002), p. 1-150.</ref> For propane, the oxygen content of an air and nitrogen mixture must be reduced below 12 % before no mixture with propane can burn.<ref name="SI-150" /> With nitrogen as the diluent, the limiting oxygen concentration of most fuels is 10 to 12 %. With carbon dioxide it is 2 to 3 percentage points higher, owing to the higher molar heat capacity of carbon dioxide.<ref name="BE-179">Beyler (2002), p. 2-179.</ref>

Diffusion flames follow a related rule. The most dilute stoichiometric premixed mixture that still propagates a flame is called the stoichiometric limit.<ref name="BE-179" /> The adiabatic flame temperature at the oxygen index of a diffusion flame is essentially equal to that at this stoichiometric limit. Both lie about 150 K above the value at the lower flammability limit in air.<ref name="BE-183">Beyler (2002), p. 2-183.</ref> For this stoichiometric limit, Beyler gives 1,700 K for most hydrocarbons, 1,450 K for carbon monoxide and 1,080 K for hydrogen.<ref name="BE-184" />

This limiting temperature underlies [[flame extinction]] by cooling. When fine water droplets from a [[Water mist system|water mist system]] evaporate in a flame, they remove heat from it. Once the flame temperature drops below the limiting adiabatic flame temperature of about 1,600 K (1,326 °C), the diffusion flame goes out.<ref name="MB-313" /> Only enough heat needs to be absorbed to reach this limiting value, so the gases do not have to be cooled to ambient temperature.<ref name="MB-313" /> The Fire Dynamics Simulator applies the same idea, under the name critical flame temperature, to decide whether combustion can continue in a grid cell.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>

Chemical inhibitors behave differently. When enough of a bromine compound is added to extinguish a stoichiometric hydrocarbon and air flame, the adiabatic flame temperature of the resulting mixture is only slightly lower than without the additive. Such compounds act as chemical inhibitors rather than as heat sinks.<ref name="SI-151">Simmons (2002), p. 1-151.</ref>

== Use in fire safety engineering ==
The limiting flame temperature allows simple checks of flammability. Drysdale describes a research engine running on methane, in which only three of the six cylinders fire. The exhaust then carries unburnt methane together with enough oxygen to burn it, and enters the exhaust duct at 700 K.<ref name="DR-97" /> If this mixture burned, its adiabatic flame temperature would be 1,749 K. That is clearly above the limiting value of 1,600 K. Drysdale concludes that there is a risk of explosion and that measures are needed to keep the mixture out of the duct.<ref name="DR-97" />

The same balance predicts how a flammability limit changes with the initial temperature. At the lower limit, the heat released by the fuel fraction of the mixture just raises the products to the limiting flame temperature:<ref name="BE-178">Beyler (2002), p. 2-178.</ref>

<math display="block">\frac{\mathrm{LFL}}{100}\,\Delta H_c = n \, C_p \left( T_{f,\mathrm{LFL}} - T_0 \right)</math>

{| class="wikitable"
|+ Symbols used in the flammability limit balance
! Symbol !! Description !! Unit
|-
| <math>\mathrm{LFL}</math> || lower flammability limit, fuel content of the mixture || % by volume
|-
| <math>\Delta H_c</math> || heat of combustion of the fuel || J/mol
|-
| <math>n</math> || moles of combustion products per mole of fuel and air mixture || –
|-
| <math>C_p</math> || average molar heat capacity of the products || J/(mol·K)
|-
| <math>T_{f,\mathrm{LFL}}</math> || adiabatic flame temperature of a lower-limit mixture || K
|-
| <math>T_0</math> || initial temperature of the mixture || K
|}

In Beyler's worked example, propane at 20 °C (293 K) has a lower flammability limit of 2.1 %. With a limiting temperature of 1,600 K, the ratio of the heat of combustion to the heat capacity of the products follows as:<ref name="BE-178" />

<math display="block">\frac{\Delta H_c}{n \, C_p} = \frac{1600 - 293}{0.021} \approx 6.22 \times 10^{4}\ \mathrm{K}</math>

At an initial temperature of 200 °C (473 K), the same ratio gives a limit fraction of (1,600 − 473)/(6.22 × 10<sup>4</sup>) = 0.0181. The lower flammability limit of propane therefore falls to 1.8 %.<ref name="BE-178" /> Flammability limits generally widen as the temperature of a mixture increases.<ref name="SI-147" /> Beyler extends the method to mixtures of fuels, and the approach has been used to predict whether the hot gas layer of an enclosure fire can ignite.<ref name="BE-184" />

In a closed vessel, the temperature rise of a burning mixture causes a matching rise in pressure. NUREG-1805 estimates the maximum pressure from the ratio of absolute temperatures:<ref name="IS-1514">Iqbal and Salley (2004), p. 15-14.</ref>

<math display="block">P_\mathrm{max} = \frac{T_\mathrm{ad}}{T_\mathrm{amb}} \, P_\mathrm{amb}</math>

Here <math>P_\mathrm{max}</math> is the maximum pressure at the end of combustion and <math>P_\mathrm{amb}</math> the initial pressure, both in kPa. <math>T_\mathrm{ad}</math> is the adiabatic flame temperature of the burnt gas and <math>T_\mathrm{amb}</math> the initial temperature of the mixture, both in K.<ref name="IS-1514" /> For a stoichiometric hydrocarbon and air mixture at 300 K, the adiabatic flame temperature of about 2,200 K gives a pressure ratio of 7.3.<ref name="SI-147" /> Starting from one standard atmosphere of 101.3 kPa, the maximum pressure becomes about 743 kPa.<ref name="IS-142">Iqbal and Salley (2004), p. 14-2.</ref> Simmons quotes a little over 7 bar for this case and notes that heat loss to the walls makes the real peak somewhat lower. A vessel not designed for such pressures will still rupture explosively.<ref name="SI-147" />

The adiabatic flame temperature also bounds the heat flux that a flame can emit. In theory, the radiant heat flux from a flame can reach <math>\varepsilon \sigma (T_f^4 - T_0^4)</math>, where <math>\varepsilon</math> is the emissivity of the flame, <math>\sigma</math> the Stefan–Boltzmann constant and <math>T_0</math> the ambient temperature. For large flames the emissivity approaches 1, and the ambient term becomes insignificant.<ref name="BA-6" /> With a Stefan–Boltzmann constant of 5.67 × 10<sup>−11</sup> kW/(m²·K⁴) and a flame temperature of about 2,300 K, this gives some 1,500 kW/m². That theoretical limit is nearly ten times the maximum found in ordinary building fires, so it offers no guidance for choosing heat fluxes in fire tests.<ref name="BA-6" />

In [[Computational fluid dynamics|computational fluid dynamics]], the adiabatic flame temperature serves as a plausibility check. Cox and Kumar describe fire sources modelled as too small a volumetric heat source, which produced predicted gas temperatures above 5,000 °C. The adiabatic flame temperature is an absolute limit on gas temperature and is unlikely to exceed about 2,000 °C.<ref name="CK-206" /> Measured time-averaged gas temperatures in fires seldom exceed around 1,300 °C. Predicted values above that level call for caution, and any value above the adiabatic flame temperature must be incorrect.<ref name="CK-206" />

== Limitations and misconceptions ==
The adiabatic flame temperature is an idealised upper bound, not a prediction of the temperature in a fire. It assumes chemical equilibrium in the burnt gas and neglects all heat losses.<ref name="SI-145" /> Hand calculations with constant, averaged heat capacities are only approximate. They overestimate the temperature when dissociation becomes important, from about 1,800 to 2,000 K upwards.<ref name="DR-96" /><ref name="SI-145" /> The relation between heat and temperature rise also holds only while the heat capacity stays roughly constant and no phase change, such as the evaporation of water, takes place.<ref name="VR-3.4" />

A frequent source of error is a tabulated value used without checking the mixture to which it refers. Stoichiometric and lower-limit values differ by several hundred kelvin.<ref name="IS-B25" /> In the table of adiabatic flame temperatures in NUREG-1805, the entries for methane (1,446 K) and propane (1,554 K) equal the lower-limit values of the SFPE Handbook. The same table lists hydrogen at 2,525 K and acetylene at 2,910 K.<ref name="IS-315" /><ref name="DR-97" /> These numbers describe different mixtures and cannot be compared directly. Input data can also differ slightly between sources: Drysdale uses a lower limit of 2.2 % for propane, whereas Beyler uses 2.1 %.<ref name="DR-96" /><ref name="BE-177" />

The limiting temperature concept has a restricted range of validity. It has been established for fuels containing carbon, hydrogen and oxygen, while no systematic evaluation exists for fuels containing sulphur, nitrogen or halogens.<ref name="BE-177" /> On the fuel-rich side, adiabatic flame temperatures can generally not be calculated. The products then include a mixture of combustion and pyrolysis products that equilibrium calculations do not predict well.<ref name="BE-177" />

The concept also fails when a mixture stays near or above its autoignition temperature long enough for reactions to start before the flame arrives. A mixture of 1 % methane in air, far below the normal lower limit of 5 %, can burn when it is preheated to 1,270 K. The flame then raises its temperature by only about 250 K.<ref name="BE-177" />

== See also ==
* [[Equivalence ratio]]
* [[Premixed flame]]
* [[Diffusion flame]]
* [[Incomplete combustion]]

== Notes ==
<references />

== References ==
* Babrauskas, V. (2002). 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.
* Beyler, C. L. (2002). Flammability limits of premixed and diffusion flames. 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. 2-172–2-187). National Fire Protection Association.
* Cox, G., & Kumar, S. (2002). Modeling enclosure fires using CFD. 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. 3-194–3-218). National Fire Protection Association.
* Drysdale, D. D. (2002). Thermochemistry. 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. 1-90–1-98). 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.
* Mawhinney, J. R., & Back, G. G., III. (2002). Water mist fire suppression systems. 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. 4-311–4-337). National Fire Protection Association.
* 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., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018
* Simmons, R. F. (2002). Premixed burning. 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. 1-144–1-154). National Fire Protection Association.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Combustion]]

← Older revision		Revision as of 23:04, 1 November 2026
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	'''Adiabatic flame temperature''' is the highest temperature that the products of a combustion reaction can reach when none of the released heat is lost to the surroundings.<ref name="DR-96">Drysdale (2002), p. 1-96.</ref><ref name="IS-315">Iqbal and Salley (2004), p. 3-15.</ref> It is a calculated value, found from an energy balance between the [[heat of combustion]] of the fuel and the heat needed to warm the products, any excess reactants and inert gases such as nitrogen.<ref name="DR-96" /> A real [[flame]] always loses heat, so its temperature stays below this ideal value.<ref name="IS-314">Iqbal and Salley (2004), p. 3-14.</ref> For most flammable gases burning in air in exactly the right proportions, the adiabatic flame temperature is about 2,300 K. Mixtures at the [[Flammability limits\|lower flammability limit]] reach only about 1,600 K.<ref name="IS-B25">Iqbal and Salley (2004), p. B-25.</ref>		'''Adiabatic flame temperature''' is the highest temperature that the products of a combustion reaction can reach when none of the released heat is lost to the surroundings.<ref name="DR-96">Drysdale (2002), p. 1-96.</ref><ref name="IS-315">Iqbal and Salley (2004), p. 3-15.</ref> It is a calculated value, found from an energy balance between the [[heat of combustion]] of the fuel and the heat needed to warm the products, any excess reactants and inert gases such as nitrogen.<ref name="DR-96" /> A real [[flame]] always loses heat, so its temperature stays below this ideal value.<ref name="IS-314">Iqbal and Salley (2004), p. 3-14.</ref> For most flammable gases burning in air in exactly the right proportions, the adiabatic flame temperature is about 2,300 K. Mixtures at the [[Flammability limits\|lower flammability limit]] reach only about 1,600 K.<ref name="IS-B25">Iqbal and Salley (2004), p. B-25.</ref>

	The second value explains why the concept matters in fire safety engineering. Many fuel mixtures cannot sustain a flame once their adiabatic flame temperature falls below a limiting value of roughly 1,600 K.<ref name="BE-177">Beyler (~~2002~~), p. 2-177.</ref><ref name="DR-97">Drysdale (2002), p. 1-97.</ref> Engineers use this limiting value to predict flammability limits, the effect of inert gases and water mist, and the risk that a hot gas layer will ignite.<ref name="MB-313">Mawhinney and Back (2002), p. 4-313.</ref><ref name="BE-184">Beyler (~~2002~~), p. 2-184.</ref> The adiabatic flame temperature also sets an upper bound for checking calculated gas temperatures, explosion pressures and radiant heat fluxes.<ref name="CK-206">Cox and Kumar (2002), p. 3-206.</ref><ref name="BA-6">Babrauskas (~~2002~~), p. 3-6.</ref>		The second value explains why the concept matters in fire safety engineering. Many fuel mixtures cannot sustain a flame once their adiabatic flame temperature falls below a limiting value of roughly 1,600 K.<ref name="BE-177">Beyler (2002b), p. 2-177.</ref><ref name="DR-97">Drysdale (2002), p. 1-97.</ref> Engineers use this limiting value to predict flammability limits, the effect of inert gases and water mist, and the risk that a hot gas layer will ignite.<ref name="MB-313">Mawhinney and Back (2002), p. 4-313.</ref><ref name="BE-184">Beyler (2002b), p. 2-184.</ref> The adiabatic flame temperature also sets an upper bound for checking calculated gas temperatures, explosion pressures and radiant heat fluxes.<ref name="CK-206">Cox and Kumar (2002), p. 3-206.</ref><ref name="BA-6">Babrauskas (2002b), p. 3-6.</ref>

	== Definition and physical meaning ==		== Definition and physical meaning ==
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	== Limiting flame temperature ==		== Limiting flame temperature ==
	The near-constant value at the lower limit has a physical explanation. A flame can only sustain itself while it produces heat faster than it loses heat, mainly by radiation. At the limit, the losses exceed the heat production and the flame can no longer propagate.<ref name="DR-97" /> As early as 1911, Burgess and Wheeler noted that lower-limit mixtures of alkanes in air release almost the same heat per unit volume. Since the products of all these fuels have nearly the same heat capacity, this observation implies a constant limiting flame temperature.<ref name="BW">Burgess and Wheeler (1911), as cited in Beyler (~~2002~~), p. 2-177.</ref> The limiting value is relatively insensitive, within about ±100 K, to the diluent used and to the initial temperature of the mixture.<ref name="BE-177" />		The near-constant value at the lower limit has a physical explanation. A flame can only sustain itself while it produces heat faster than it loses heat, mainly by radiation. At the limit, the losses exceed the heat production and the flame can no longer propagate.<ref name="DR-97" /> As early as 1911, Burgess and Wheeler noted that lower-limit mixtures of alkanes in air release almost the same heat per unit volume. Since the products of all these fuels have nearly the same heat capacity, this observation implies a constant limiting flame temperature.<ref name="BW">Burgess and Wheeler (1911), as cited in Beyler (2002b), p. 2-177.</ref> The limiting value is relatively insensitive, within about ±100 K, to the diluent used and to the initial temperature of the mixture.<ref name="BE-177" />

	The same concept describes the effect of inert gases. Nitrogen, argon and carbon dioxide lower the final flame temperature, and if the burning velocity falls far enough, the flame goes out.<ref name="SI-150">Simmons (2002), p. 1-150.</ref> For propane, the oxygen content of an air and nitrogen mixture must be reduced below 12 % before no mixture with propane can burn.<ref name="SI-150" /> With nitrogen as the diluent, the limiting oxygen concentration of most fuels is 10 to 12 %. With carbon dioxide it is 2 to 3 percentage points higher, owing to the higher molar heat capacity of carbon dioxide.<ref name="BE-179">Beyler (~~2002~~), p. 2-179.</ref>		The same concept describes the effect of inert gases. Nitrogen, argon and carbon dioxide lower the final flame temperature, and if the burning velocity falls far enough, the flame goes out.<ref name="SI-150">Simmons (2002), p. 1-150.</ref> For propane, the oxygen content of an air and nitrogen mixture must be reduced below 12 % before no mixture with propane can burn.<ref name="SI-150" /> With nitrogen as the diluent, the limiting oxygen concentration of most fuels is 10 to 12 %. With carbon dioxide it is 2 to 3 percentage points higher, owing to the higher molar heat capacity of carbon dioxide.<ref name="BE-179">Beyler (2002b), p. 2-179.</ref>

	Diffusion flames follow a related rule. The most dilute stoichiometric premixed mixture that still propagates a flame is called the stoichiometric limit.<ref name="BE-179" /> The adiabatic flame temperature at the oxygen index of a diffusion flame is essentially equal to that at this stoichiometric limit. Both lie about 150 K above the value at the lower flammability limit in air.<ref name="BE-183">Beyler (~~2002~~), p. 2-183.</ref> For this stoichiometric limit, Beyler gives 1,700 K for most hydrocarbons, 1,450 K for carbon monoxide and 1,080 K for hydrogen.<ref name="BE-184" />		Diffusion flames follow a related rule. The most dilute stoichiometric premixed mixture that still propagates a flame is called the stoichiometric limit.<ref name="BE-179" /> The adiabatic flame temperature at the oxygen index of a diffusion flame is essentially equal to that at this stoichiometric limit. Both lie about 150 K above the value at the lower flammability limit in air.<ref name="BE-183">Beyler (2002b), p. 2-183.</ref> For this stoichiometric limit, Beyler gives 1,700 K for most hydrocarbons, 1,450 K for carbon monoxide and 1,080 K for hydrogen.<ref name="BE-184" />

	This limiting temperature underlies [[flame extinction]] by cooling. When fine water droplets from a [[Water mist system\|water mist system]] evaporate in a flame, they remove heat from it. Once the flame temperature drops below the limiting adiabatic flame temperature of about 1,600 K (1,326 °C), the diffusion flame goes out.<ref name="MB-313" /> Only enough heat needs to be absorbed to reach this limiting value, so the gases do not have to be cooled to ambient temperature.<ref name="MB-313" /> The Fire Dynamics Simulator applies the same idea, under the name critical flame temperature, to decide whether combustion can continue in a grid cell.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>		This limiting temperature underlies [[flame extinction]] by cooling. When fine water droplets from a [[Water mist system\|water mist system]] evaporate in a flame, they remove heat from it. Once the flame temperature drops below the limiting adiabatic flame temperature of about 1,600 K (1,326 °C), the diffusion flame goes out.<ref name="MB-313" /> Only enough heat needs to be absorbed to reach this limiting value, so the gases do not have to be cooled to ambient temperature.<ref name="MB-313" /> The Fire Dynamics Simulator applies the same idea, under the name critical flame temperature, to decide whether combustion can continue in a grid cell.<ref name="MG-62">McGrattan et al. (2026), p. 62.</ref>
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	The limiting flame temperature allows simple checks of flammability. Drysdale describes a research engine running on methane, in which only three of the six cylinders fire. The exhaust then carries unburnt methane together with enough oxygen to burn it, and enters the exhaust duct at 700 K.<ref name="DR-97" /> If this mixture burned, its adiabatic flame temperature would be 1,749 K. That is clearly above the limiting value of 1,600 K. Drysdale concludes that there is a risk of explosion and that measures are needed to keep the mixture out of the duct.<ref name="DR-97" />		The limiting flame temperature allows simple checks of flammability. Drysdale describes a research engine running on methane, in which only three of the six cylinders fire. The exhaust then carries unburnt methane together with enough oxygen to burn it, and enters the exhaust duct at 700 K.<ref name="DR-97" /> If this mixture burned, its adiabatic flame temperature would be 1,749 K. That is clearly above the limiting value of 1,600 K. Drysdale concludes that there is a risk of explosion and that measures are needed to keep the mixture out of the duct.<ref name="DR-97" />

	The same balance predicts how a flammability limit changes with the initial temperature. At the lower limit, the heat released by the fuel fraction of the mixture just raises the products to the limiting flame temperature:<ref name="BE-178">Beyler (~~2002~~), p. 2-178.</ref>		The same balance predicts how a flammability limit changes with the initial temperature. At the lower limit, the heat released by the fuel fraction of the mixture just raises the products to the limiting flame temperature:<ref name="BE-178">Beyler (2002b), p. 2-178.</ref>

	<math display="block">\frac{\mathrm{LFL}}{100}\,\Delta H_c = n \, C_p \left( T_{f,\mathrm{LFL}} - T_0 \right)</math>		<math display="block">\frac{\mathrm{LFL}}{100}\,\Delta H_c = n \, C_p \left( T_{f,\mathrm{LFL}} - T_0 \right)</math>
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	== References ==		== References ==
	* Babrauskas, V. (~~2002~~). 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.		* 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.
	* Beyler, C. L. (~~2002~~). Flammability limits of premixed and diffusion flames. 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. 2-172–2-187). National Fire Protection Association.		* Beyler, C. L. (2002b). Flammability limits of premixed and diffusion flames. 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. 2-172–2-187). National Fire Protection Association; Society of Fire Protection Engineers.
	* Cox, G., & Kumar, S. (2002). Modeling enclosure fires using CFD. 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. 3-194–3-218). National Fire Protection Association.		* Cox, G., & Kumar, S. (2002). Modeling enclosure fires using CFD. 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. 3-194–3-218). National Fire Protection Association; Society of Fire Protection Engineers.
	* Drysdale, D. D. (2002). Thermochemistry. 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. 1-90–1-98). National Fire Protection Association.		* Drysdale, D. D. (2002). Thermochemistry. 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. 1-90–1-98). 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.		* 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.
	* Mawhinney, J. R., & Back, G. G., III. (2002). Water mist fire suppression systems. 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. 4-311–4-337). National Fire Protection Association.		* Mawhinney, J. R., & Back, G. G., III. (2002). Water mist fire suppression systems. 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. 4-311–4-337). National Fire Protection Association; Society of Fire Protection Engineers.
	* 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., NIST Special Publication 1018-1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.SP.1018		* 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
	* Simmons, R. F. (2002). Premixed burning. 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. 1-144–1-154). National Fire Protection Association.		* Simmons, R. F. (2002). Premixed burning. 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. 1-144–1-154). National Fire Protection Association; Society of Fire Protection Engineers.
	* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.		* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

	[[Category:Combustion]]		[[Category:Combustion]]