Mathematical Problems in Engineering 
Volume 3 (1997), Issue 4, Pages 373-385
doi:10.1155/S1024123X97000604

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

Abstract

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=(Tb−Tu)/Tu, of order β−1/2, 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.