Solution of Condensed Phase Equations

The condensed phase energy equation, being decoupled from the species 

An approximate expression which is widely used instead is 

These equations are commonly called pyrolysis relations, in reference to the thermal (as opposed to a possibly chemical or photonic) nature of the initiating step(s) in the condensed phase decomposition process. It can be seen that while the second, simpler pyrolysis expression with constant coefficient As) preserves the important Arrhenius exponential temperature dependent term, it ignores the effect of the initial temperature, condensed phase heat release and thermal radiation parameters present in the more comprehensive zero-order pyrolysis relation. These terms To, Qc, and qr) make a significant difference when it comes to sensitivity parameter and unsteady combustion considerations. It is also important to note the factor of 2, which relates the apparent surface activation energy Es to the actual bulk activation energy Ec, Es- E /1. Failure to recognize this factor of two hindered progress in some cases as attempts were 

The pyrolysis equations above are based on an assumed which is not generally known from condensed phase considerations alone. To proceed further and obtain a solution for mass flux requires information about the conductive heat feedback to the surface from the gas phase qc which must be supplied by the gas 

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