ON THE STRUCTURE OF A DISTINGUISHED-LIMIT QUASI-ISOTHERMAL DEFLAGRATION FOR THE GENERALIZED REACTION-RATE MODEL

The structure of the quasi-isothermal deflagration is examined by mean s of an asymptotic analysis of the physical-plane boundary-value probl em, with Lewis-Semenov number unity, in the limit of the activation-te mperature ratio, beta = T-a/T-b, greater than order unity, for the gen eralized reaction-rate-model case of: (1) the heat-addition-temperatur e ratio, alpha=(T-b-T-u)/T-u, of order beta(-1/2), less than order uni ty [where T-a, T-b, and T-u are the activation, adiabatic-flame (and/o r burned-gas), and unburned-gas temperatures, respectively]; and (2) t he exponent, a, which characterizes the pre-exponential thermal depend ence of the reaction-rate term, unity. The examination indicates that, as in the order-unity heat-addition case, this deflagration has a fou r-region structure: the upstream diffusion-convection and downstream d iffusion-reaction regions, and the far-upstream (or cold-boundary) and the far-downstream (or hot-boundary) regions.