On the structure of a distinguished-limit quasi-isothermal deflagration for the generalized reaction-rate model (Q1267831)

Summary: We examine the structure of the quasi-isothermal deflagration by means of an asymptotic analysis of the physical-plane boundary value problem, with Lewis-Semenov number unity, in the limit of the activation-temperature ratio, \(\beta= T_a/T_b\), greater than order unity. We consider the generalized reaction-rate model where: (1) the heat-addition-temperature ratio, \(\alpha= (T_b- T_u)/T_u\), of order \(\beta^{-1/2}\), is less than order unity (where \(T_a\), \(T_b\), and \(T_u\) are the activation, adiabatic-flame (and/or burned-gas), and unburned-gas temperatures, respectively); and (2) the exponent, \(a\), which characterizes the pre-exponential thermal dependence of the reaction-rate term, is equal to unity. The examination indicates that, as in the order-unity heat-addition case, the deflagration has a four-region structure: the upstream diffusion-convection and downstream diffusion-reaction regions, and the far-upstream (or cold-boundary) and the far-downstream (or hot-boundary) regions.