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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, J.H. Merkin and 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 λ 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 λ. This latter solution shows the existence of a propagating reaction-diffusion burning wave.
MSC:
76V05Interacting phases (fluid mechanics)
80A25Combustion, interior ballistics
35K57Reaction-diffusion equations