Thermal feedback ignition, extinction and singularity theory

5 THERMAL FEEDBACK IGNITION, EXTINCTION AND SINGULARITY THEORY 

Here A is the pre-exponential factor, E is an effective activation energy or temperature coefficient for the overall reaction, R = 8.314 JK moP is the Gas Constant and T is the local absolute temperature. The quotient E/R has units of temperature and is sometimes known as the Arrhenius temperature It is a characteristic feature of combustion processes that if Ta is the ambient temperature, then Tatt so that the group RTJE and, more generally, the scaled or dimensionless temperature RTIE are typically (very) small quantities in the systems of interest. 

The evolution of the local temperature in a reacting system is governed by the heat balance equation. This may become quite complex in unstirred systems, especially if convective heat transfer processes develop as a consequence of local heating. For the simple CSTR described earlier we can proceed with an ordinary differential equation of the form 

For the simplest chemical case imaginable, that of a single first-order reaction 

Arrhenius form given above, the two governing equations for reaction in a CSTR have the form 

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