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Mathematical Problems in Engineering
Volume 2, Issue 5, Pages 435-447
http://dx.doi.org/10.1155/S1024123X96000427

On the structure of the deflagration for the generalized reaction-rate model

1King, Buck & Associates, Inc., San Diego, CA 92110, USA
2Florida Institute of Technology, Melbourne, FL 32901, USA

Received 15 January 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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=(TbTu)/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.