On the stability of a stationary front of an exothermic reaction in cylindrical samples

Abstract

The problem of the stability of a planar combustion wave front which propagates in a thermally isolated porous cylinder is considered. A model system of the theory of combustion is used which describes an exothermic reaction in a porous medium saturated with gas. The Arrhenius dependence of the reaction rate is replaced by a piecewise-constant dependence. In this case it is possible to find an analytical solution for the temperature distribution and the distribution of the reagent concentration in the stationary wave. Unlike the results obtained using the approach in /1, 2/, the thermal and diffusion fluxes are continuous everywhere in the case of the solution which is constructed. Investigation of the stability of the solution leads to results which are similar to the approximate results in /1, 2/ but the details concerning loss of stability exhibit a qualitative difference associated with the occurrence of folding in the neighbourhood of the neutral hypersurface at a Lewis number L< 1 which accounts for the possible appearance of vortex waves in a sample of circular cross-section /3, 4/.