Combustion model, autocatalytic reaction

Mathematical Model of Combustion in the Case of Autocatalytic Reaction... 

IX. MATHEMATICAL MODEL OF COMBUSTION IN THE CASE OF AUTOCATALYTIC REACTION... 

We consider the case of a unique scalar reactive field 0(jc, t). This model is appropriate in aqueous autocatalytic premixed reactions, as well as in gaseous combustion with a large flow intensity but low value of gas expansion across the flame [7]. The field 0 evolves according to the advection-reaction-diffusion (ARD) equation ... 

Specific examples of such bistable behavior arise in models of combustion. In the simplest case, a two-component system, that includes the distribution of the fuel and of the temperature field, is appropriate. The reaction takes place only when the temperature is above a certain ignition temperature, with a burning rate that is an increasing function of the local temperature following the Arrhenius law (Eq. (3.43)). The burning of fuel is an exothermic reaction that increases the local temperature and results in even higher reaction rates. This leads to the autocatalytic character of the system, while the ignition temperature acts as a threshold, responsible for the bistability. 

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