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What defines the adiabatic flame temperature?

In a case I have to solve, I need to describe the combustion of natural gas (Groningen natural gas, to be specific). However, I am having some problems understanding the adiabatic flame temperature, since on the internet I find some temperatures, but to me it seems that it would depend on the initial conditions, such as the start temperature and the fuel-oxidizer mixture.

The combustion should take place inside a ceramic foam, and I am assuming that this would happen isobaric at atmospheric pressure, and the inserted gas mixture before combustion would be at room temperature. I need to describe a stationary situation, in which the flue gas will lose a certain amount of heat according to a given formula to foam (which will emit the same amount of energy through thermal radiation).

Would the adiabatic flame temperature be equal to the temperature of the exhaust gas before the heat loss to the ceramic foam?

$$ {\Delta}T=\frac{Q}{c_p}, $$ with ${\Delta}T$ the increase in temperature of the exhaust gas (relative to the temperature of the inserted fuel-oxidizer mixture) and $Q$ the net calorific value of the gas (taking in to account that the amount of moles change during the combustion). Or is the adiabatic flame temperature something completely different?

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The adiabatic flame temperature $T_f$ is implicitly given by $h_f^n=h_i^n+\int_{T_i}^{T_f}c_p^n\text d T$ where $h^n$ is the enthalpy of the species $n$ and $i/f$ denote initial/final. However, if the system loses heat to the surroundings, I think computing the adiabatic flame temperature is questionable. The derivation of the integral expression, afaik, relies on $\sum_nh_f^n=\sum_nh_i^n$. The formula you wrote down might be the difference between the final temperature of the gas (heat loss included) and the temperature value you would get if you had an adiabatic combustion +$c_p$ const. –  NikolajK May 2 '13 at 12:45
    
Thanks for your reply. But up to now I haven't been able to find all the initial enthalpy values of each component (at 298 K). That is why I assumed that the enthalpy level at 298 K for the fuel-oxidizer mixture would be equal to the enthalpy level at 298 K for the exhaust gasses, however this is probably falls. The enthalpy values I did found for the hydrocarbon fuels are the formation enthalpy values. And for the cp I have a table in which it is given for certain for certain temperature steps (the average cp). –  fibonatic May 2 '13 at 16:02
    
By the way your explanation this doesn't explain why the given the adiabatic flame temperature are given as constants in the literature for stoichiometric combustion with air (79% N2 and 21% O2), to me it would still seem that the initial temperature would affect this. –  fibonatic May 2 '13 at 16:27

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Your understanding about adiabatic flame temperature is correct conceptually, though the mathematical representation of adiabatic flame temperature you have given is just an approximation which again is sufficiently accurate for most of the practical purposes. You can make it more accurate by expressing the specific heats of the flue gases (assuming the mixture as $N_2$, $CO_2$, $O_2$) as a function of temperature. Of course you will have to iterate it a few times to get the final value. You will also have to use a mixing rule to compute the effective heat capacity of the mixture of gases. In fact the concentration of components vary with time during the process of heat generation, but you can take the final concentration for computational purposes.

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