Reaction‐driven convection in a porous medium

Abstract

Abstract The onset of three‐dimensional reaction‐driven convection in a porous medium is investigated using linear stability theory. The geometries investigated include a finite cylinder and a rectangular parallelepipped of arbitrary aspect ratios. The analysis determines, among other things, the likely modes (flow patterns) to emerge first as a function of reaction parameters and aspect ratios. The flow fields corresponding to three‐dimensional modes are described in detail. Important qualitative differences are found between reaction‐driven convection and the standard Lapwood or Bénard convection due to a temperature gradient applied to the boundaries of the system. The second part of the work examines numerically reaction‐driven natural convection in a porous two‐dimensional rectangular box. Orthogonal collocation and continuation techniques are used to determine the conduction and convection branches of solutions as a function of the Rayleigh number (Ra), the Frank‐Kamenetskii number (δ) and the aspect ratio (α). The convective solutions (streamlines and isotherms) corresponding to primary, secondary and tertiary bifurcations are presented. The effect of natural convection (Ra) on the ignition point (critical δ value) is determined for three different aspect ratios.