Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Mathematical Problems in Engineering

Abstract

The structure of the deflagration is examined 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, β = Ta/Tb, greater than order unity, for the generalized reaction-rate-model case of (1) the heat- addition-temperature ratio, α = (Tb — Tu)/Tu, of order unity [where Ta, Tb, and Tu 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, unity. This examination indicates that the deflagration has a four-region structure. To obtain a uniformly valid solution of the problem, in addition to the (classical) upstream diffusion-convection and downstream diffusion-reaction regions, a far-upstream (or cold-boundary) region and a far-downstream (or hot-boundary) region must be introduced.

First Page

435

Last Page

447

DOI

10.1155/S1024123X96000427

Publication Date

1996

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