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Reaction-diffusion model for combustion with fuel consumption. II: Robin boundary conditions. (English) Zbl 0786.76100

A model, derived in a previous paper [G. Zhang et al., IMA J. Appl. Math. 47, No. 1, 33–60 (1991; Zbl 0775.76214)], for the reaction between a gaseous oxidant and a solid porous fuel is analysed for general Robin boundary conditions. Numerical solutions are obtained and the effects of varying the dimensionless parameters, particularly the Frank-Kamenetskij parameter \(\lambda\) and the Lewis number \(L\), are discussed in detail and compared with results obtained previously when Dirichlet boundary conditions are applied. Analytic solutions are obtained for the small-time development and for large values of \(\lambda\). This latter solution shows the existence of a propagating reaction-diffusion burning wave.

MSC:

76V05 Reaction effects in flows
80A25 Combustion
35K57 Reaction-diffusion equations

Citations:

Zbl 0775.76214
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