Adiabatic flame temperature

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. 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. A real flame always loses heat, so its temperature stays below this ideal value. For most flammable gases burning in air in exactly the right proportions, the adiabatic flame temperature is about 2,300 K. Mixtures at the lower flammability limit reach only about 1,600 K.

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. 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. The adiabatic flame temperature also sets an upper bound for checking calculated gas temperatures, explosion pressures and radiant heat fluxes.

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. 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. 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.

The concept is closely tied to stoichiometry, which describes the proportions in which substances are consumed and formed in a chemical reaction. 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. 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.

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. 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. Small premixed flames and turbulent flames of all kinds normally fall short of it, because their heat losses are appreciable.

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. In equation form this balance reads:

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.

$$\mathrm{\Delta }{H}_r^0=\underset{T_i}{\overset{T_f}{\int }}{C}_p\mathrm{d}T$$

The heat capacity in this integral covers all of the product gases, including excess oxygen and nitrogen. The calculation neglects every heat loss from the flame, whether by radiation, by conduction or by diffusion to a wall. 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.

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:

$$\mathrm{\Delta }T=T_f-T_i=\frac{\mathrm{\Delta }{H}_c}{\sum _j{n}_j{C}_{p,j}}$$

Symbols used in the energy balance

Symbol	Description	Unit
$\mathrm{\Delta }{H}_r^0$	heat released by the reaction at the initial temperature, per mole of fuel	J/mol
$\mathrm{\Delta }{H}_c$	heat of combustion per mole of fuel	J/mol
$T_i$	initial temperature of the reactants	K
$T_f$	final (adiabatic) flame temperature	K
$\mathrm{\Delta }T$	temperature rise of the products	K
$C_p$	heat capacity of the products at constant pressure, per mole of fuel	J/(mol·K)
$n_j$	number of moles of product gas j formed per mole of fuel	–
$C_{p,j}$	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. The overall reaction is:

$${\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{8}}+5{\mathrm{O}}_{\mathrm{2}}+18.8{\mathrm{N}}_{\mathrm{2}}\to 3\mathrm{C}{\mathrm{O}}_{\mathrm{2}}+4{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+18.8{\mathrm{N}}_{\mathrm{2}}$$

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. The temperature rise then follows directly from the division:

$$\mathrm{\Delta }T=\frac{2.044\times 10^6\mathrm{J}}{942.5\mathrm{J}/\mathrm{K}}\approx 2169\mathrm{K}$$

Heat capacity of the products per mole of propane, at 1,000 K

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. 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.

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.

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. 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. Chemical equilibrium programs such as STANJAN can calculate the adiabatic flame temperature of a specific mixture, for example the contents of a particular tank. For lean mixtures with relatively low flame temperatures, the products follow directly from the overall stoichiometry, and the simple method is adequate.

Real flame temperatures

Measured flame temperatures in fires lie far below the adiabatic values. 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. 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. In a candle flame, which is a laminar diffusion flame, the outer zone is the hottest part and reaches about 1,400 °C.

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. 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.

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. In a burner flame of 7.5 % natural gas in air, the highest measured temperature contour lies at 1,755 °C. 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.

Typical values

For most flammable gases at atmospheric pressure, a stoichiometric mixture with air has an adiabatic flame temperature of about 2,300 K. Simmons quotes about 2,200 K for a stoichiometric hydrocarbon and air mixture with an initial temperature of 300 K. Babrauskas gives approximately 2,300 K for most organic fuels. 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 %. For the other hydrocarbon gases, the limiting value lies in a narrow band of 1,600 ± 100 K.

Adiabatic flame temperature of hydrocarbon and air mixtures at the lower flammability limit

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. 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. Fuels that contain halogens have limit temperatures several hundred degrees higher. This agrees with the role of halogens as combustion inhibitors.

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

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. 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. The limiting value is relatively insensitive, within about ±100 K, to the diluent used and to the initial temperature of the mixture.

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. For propane, the oxygen content of an air and nitrogen mixture must be reduced below 12 % before no mixture with propane can burn. 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.

Diffusion flames follow a related rule. The most dilute stoichiometric premixed mixture that still propagates a flame is called the stoichiometric limit. 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. For this stoichiometric limit, Beyler gives 1,700 K for most hydrocarbons, 1,450 K for carbon monoxide and 1,080 K for hydrogen.

This limiting temperature underlies flame extinction by cooling. When fine water droplets from a 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. Only enough heat needs to be absorbed to reach this limiting value, so the gases do not have to be cooled to ambient temperature. The Fire Dynamics Simulator applies the same idea, under the name critical flame temperature, to decide whether combustion can continue in a grid cell.

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.

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. 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.

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:

$$\frac{\mathrm{L}\mathrm{F}\mathrm{L}}{100}\mathrm{\Delta }{H}_c=n{C}_p(T_{f,\mathrm{L}\mathrm{F}\mathrm{L}}-T_0)$$

Symbols used in the flammability limit balance

Symbol	Description	Unit
$\mathrm{L}\mathrm{F}\mathrm{L}$	lower flammability limit, fuel content of the mixture	% by volume
$\mathrm{\Delta }{H}_c$	heat of combustion of the fuel	J/mol
$n$	moles of combustion products per mole of fuel and air mixture	–
$C_p$	average molar heat capacity of the products	J/(mol·K)
$T_{f,\mathrm{L}\mathrm{F}\mathrm{L}}$	adiabatic flame temperature of a lower-limit mixture	K
$T_0$	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:

$$\frac{\mathrm{\Delta }{H}_c}{n{C}_p}=\frac{1600-293}{0.021}\approx 6.22\times 10^4\mathrm{K}$$

At an initial temperature of 200 °C (473 K), the same ratio gives a limit fraction of (1,600 − 473)/(6.22 × 10⁴) = 0.0181. The lower flammability limit of propane therefore falls to 1.8 %. Flammability limits generally widen as the temperature of a mixture increases. 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.

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:

$$P_{\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{T_{\mathrm{a}\mathrm{d}}}{T_{\mathrm{a}\mathrm{m}\mathrm{b}}}{P}_{\mathrm{a}\mathrm{m}\mathrm{b}}$$

Here $P_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum pressure at the end of combustion and $P_{\mathrm{a}\mathrm{m}\mathrm{b}}$ the initial pressure, both in kPa. $T_{\mathrm{a}\mathrm{d}}$ is the adiabatic flame temperature of the burnt gas and $T_{\mathrm{a}\mathrm{m}\mathrm{b}}$ the initial temperature of the mixture, both in K. 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. Starting from one standard atmosphere of 101.3 kPa, the maximum pressure becomes about 743 kPa. 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.

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 $\epsilon \sigma (T_f^4-T_0^4)$, where $\epsilon$ is the emissivity of the flame, $\sigma$ the Stefan–Boltzmann constant and $T_0$ the ambient temperature. For large flames the emissivity approaches 1, and the ambient term becomes insignificant. With a Stefan–Boltzmann constant of 5.67 × 10⁻¹¹ 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.

In 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. 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.

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. 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. 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.

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. 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. 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 %.

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. 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.

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.

See also

• Equivalence ratio
• Premixed flame
• Diffusion flame
• Incomplete combustion

References

• 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. (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; 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; 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.
• 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: 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; Society of Fire Protection Engineers.
• Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.