ON THE STRUCTURE OF THE DEFLAGRATION FOR THE GENERALIZED REACTION-RATE MODEL

• Published in: Mathematical Problems in Engineering Vol. 1996; no. 5; pp. 435 - 447
• Main Authors: Bush, W. B., Krishnamurthy, L.
• Format: Journal Article
• Language: English
• Published: Hindawi Limiteds 01.01.1996
• Subjects: cold-boundary difficulty; laminar deflagration; Activation-energy asymptotics
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/S1024123X96000427

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 = T_a/T_b, greater than order unity, for the generalized reaction-rate-model case of (1) the heataddition-temperature ratio, α = (T_b - T_u)/T_u, of order unity [where T_a, T_b, and T_u 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.