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

• Main Authors: W. B. Bush, L. Krishnamurthy
• Format: Article
• Language: English
• Published: Hindawi Limited 1997-01-01
• Series: Mathematical Problems in Engineering
• Subjects: Activation-energy asymptotics; Cold-boundary difficulty; Laminar deflagration; Quasi-isothermal.
• Online Access: http://dx.doi.org/10.1155/S1024123X97000604
• ISSN: 1024-123X; 1563-5147

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.