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Critical behaviour in a three-step reaction kinetics model. (English) Zbl 1156.80401
Summary: We examine the role of a more detailed chemistry comprising the initiation, branching/propagation and termination steps in the theory of combustion, formulated on some class A geometries. This is with a view to investigating the impact of the termination reaction step, which is exothermic, and the temperature-dependent pre-exponential factor, on the critical behaviour of the system. Using an effective activation energy (EAE) approximation, the stationary nonlinear governing heat equation is analysed using a variational method implemented in the Mathematica package. In addition, using an adiabatic approximation, an expression for the ignition time was obtained for the homogeneous system. The effects of the termination reaction step and variable pre-exponential factor on the thermal ignition parameters were established. Apart from validating known results, the results obtained gave further insight into the behaviour of the system.

MSC:
80A25 Combustion
80A32 Chemically reacting flows
80M30 Variational methods applied to problems in thermodynamics and heat transfer
Software:
Mathematica
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