Adiabatic Flame Temperature

Normally when a fuel burns, the energy of combustion goes partly into raising the temperature of the exhaust gases, and partly into heat that is removed from the reactants via conduction, convection, and radiation.  It is often helpful to consider the two extremes of this process:
(1) How much heat would be obtainable if you could remove so much that the exhaust gases came out at the same temperature as the reactants started at? 
(2) How hot would the exhaust gases get if you removed NO heat whatsoever?
The answer to that second question is called the adiabatic flame temperature, and it is the subject of our post today.
From conservation of energy the adiabatic flame temperature is the highest possible temperature that could possibly be reached for that particular reaction. It depends on the completeness of the reaction (if there is unburned fuel, or unburned intermediates, there is more heat that could have been released), the amount of air (not enough air leaves some unburned fuel, and too much air absorbs some of the heat) and the components of the reaction (a fuel burned in pure oxygen could reach a higher temperature than one burned in air).
While the adiabatic flame temperature is the maximum temperature for a given reaction, the highest adiabatic flame temperature (the maximum of the maximums, so to speak) occurs in a stoichiometric (which means that there is the exact amount of air necessary to burn all of the fuel)  reaction with complete combustion.
This table shows the adiabatic flame temperature for a few different fuels.

 This figure shows the adiabatic flame temperature for octane (C₈H₁₈, a common approximation for gasoline) as a function of the fraction of stoichiometric air.

 For the case shown, the temperature of the reactants was assumed to be 25 deg C.  For amounts of air less than stoichiometric  (fuel rich), the exhaust gases are assumed to contain CO₂, H₂O, CO, and N₂.  For amounts of air greater than stoichiometric (fuel lean) the exhaust gases are assumed to contain CO₂, H₂O, O₂, and N₂.  For stoichiometric combustion, the exhaust gases just contain CO₂, H₂O, and N₂. 
The peak occurs for stoichiometric air at 2362 K.  The rich (left side) and lean (right side) lines are fit very well with this equation:
AFT(K)=a + b*ta + c*ta²
Where “ta” is the theoretical air (fraction of air compared to the amount required for stoichiometric combustion), and the coefficients are shown in this table:

                                  (0.7<=ta<=1.3)
Finally, you might expect that if the temperature of the reactants goes up, the adiabatic flame temperature would go up as well.  This is true, but it doesn’t go up the exact same amount as the input temperature because the variations in material properties are not entirely linear.  The adiabatic flame temperature as a function of both theoretical air and input temperature (T_in, in K) can be estimated with this equation, where the coefficients are provided in the table below:
AFT(K)=A + B*ta  + C*ta²  + D*T_in + E*T_in² 

                                   (0.7<=ta<=1.3, 250K<=T_in<=850K)