REACTION DIFFUSION-MODEL FOR COMBUSTION WITH FUEL CONSUMPTION .1. DIRICHLET BOUNDARY-CONDITIONS

A model is derived for the reaction between a gaseous oxidant and a solid porous fuel, which allows for the consumption of the fuel. A single exothermic reaction, first-order in the concentration of the oxidant and fuel with an Arrhenius temperature dependence of the reaction rate constant is assumed. The solid reactant is taken to have an infinite slab geometry and be surrounded by a reservoir of constant oxidant concentration and fixed ambient temperature. Numerical solutions of the governing equations are obtained and the effects of varying the dimensionless parameters, especially the Frank-Kamenetskii parameter lambda and the Lewis number L, are examined. Analytic solutions are then derived for the initial development of the solution and for large values of lambda. This latter solution shows the development of a reaction-diffusion wave which starts at the edge and propagates across the slab, the structure of which depends on the Lewis number.