Mathematical Problems in Engineering

Mathematical Problems in Engineering / 1997 / Article

Open Access

Volume 3 |Article ID 156759 | https://doi.org/10.1155/S1024123X97000604

W. B. Bush, L. Krishnamurthy, "On the structure of a distinguished-limit quasi-isothermal deflagration for the generalized reaction-rate model", Mathematical Problems in Engineering, vol. 3, Article ID 156759, 13 pages, 1997. https://doi.org/10.1155/S1024123X97000604

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

Received04 Feb 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=(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.

Copyright © 1997 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.


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