Analysis and classification of reaction-driven stationary convective patterns in a porous medium

Abstract

A two-dimensional model consisting of continuity, momentum, species, and energy balances is considered to analyze the convective patterns that arise due to exothermic reactions occurring in a porous medium. First, the one-dimensional conduction states of the system are classified using singularity theory and the shooting technique. It is observed that there can be either one or three conduction states when the reacting fluid is a gas. Next, we use linear stability analysis to determine the boundary of the parameter values at which the conduction state loses stability leading to convective flows. Pure and mixed-mode convective solutions are then analyzed using local bifurcation theory. The formulas to evaluate the coefficients appearing in the amplitude equations are developed and used to obtain the classification (phase) diagram of the convective flows in the parameter space. The classification is presented in the unique conduction solution region in the presence and absence of mode interactions. The phase diagrams are used to identify the region of parameter values where convection has a detrimental effect on the stability of the system. It is found that the Lewis number (Le), which represents the ratio of thermal to mass diffusivity, has a profound influence on the stability boundaries. For Le>1, the convective solutions may bifurcate subcritically and introduce an ignition point.