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Zbl 0786.76100
Zhang, G.; Merkin, J.H.; Scott, S.K.
Reaction-diffusion model for combustion with fuel consumption. II: Robin boundary conditions. (English)
[J] IMA J. Appl. Math. 51, No.1, 69-93 (1993). ISSN 0272-4960; ISSN 1464-3634/e

A model, derived in a previous paper [{\it G. Zhang}, {\it J.H. Merkin} and {\it S. K. Scott}, IMA J. Appl. Math. 47, 33-60 (1991)], 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 2000:: *76V05 Interacting phases (fluid mechanics)
80A25 Combustion, interior ballistics
35K57 Reaction-diffusion equations

Keywords: gaseous oxidant; solid porous fuel; Frank-Kamenetskij parameter; reaction-diffusion burning wave

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Zentralblatt MATH Berlin [Germany]