Mathematical Problems in Engineering
Volume 2 (1996), Issue 5, Pages 435-447

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

W. B. Bush1 and L. Krishnamurthy2

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

Received 15 January 1996

Copyright © 1996 W. B. Bush and L. Krishnamurthy. 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.


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.