Mathematical Problems in Engineering
Volume 3 (1997), Issue 4, Pages 373-385

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

W. B. Bush1 and L. Krishnamurthy2

1King Buck & Associates, Inc., San Diego 92110, CA, USA
2Aerospace Engineering Program, Florida Institute of Technology, Melbourne 32901-6988, FL, USA

Received 4 February 1997

Copyright © 1997 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 quasi-isothermal 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 β1/2, less than 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. The examination indicates that, as in the order-unity heat-addition case, this 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.