The adiabatic temperature rise

If you are solving the heat balances of all three basic reactor types for the adiabatic case, you get 'amazingly' the same solution:

Do you know that the conversion U is coming from the reaction term and are you able to derive this formula ? Not ? (word.doc derived htm!!)

If you write: T = T0 + Tad * U A
you see the definition of Tad:
Tad is the temperature that can be reached in an adiabatic reaction for full conversion, it is the maximum of heat you can expect in this case, it depends mainly on the reaction enthalpy. For lower conversions you get a 'partial' adiabatic temperature rise following the formula. The adiabatic temperature rise is a linear function of the conversion (don't change that with the reaction time, as U is not a linear function of reaction time!!)
see link!!

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