Convective instabilities induced by exothermic reactions occurring in a porous medium

A pseudohomogeneous model is developed and used to analyze the onset of reaction-driven convection in an open rectangular box containing a porous medium. For exothermic reactions, the one-dimensional conduction state exhibits multiplicity as well as oscillatory behavior. Singularity theory is used to classify the different possible bifurcation diagrams of conduction states, along with their stabilities. Linear instability theory is used to determine the stability of the conduction states to convective perturbations. The dependence of both simple zero and Hopf bifurcation neutral stability curves on various problem parameters is presented. It is shown that the Lewis number, Le (ratio of thermal to mass diffusivity), has a pronounced effect on the stability boundaries. Increasing the value of Le, shifts the stationary stability boundary toward higher Rayleigh numbers (Ra). It is also shown that in the region of multiple conduction solutions, there exists a critical value of Lewis number, Le1 (resp., Le2) below which the entire ignited (resp., extinguished) conduction branch is stable to convective perturbations for 0