Anisotropy effect on the convection of a heat-conducting fluid in a porous medium and cosymmetry of the Darcy problem

Abstract

The onset of convection in a porous rectangle is analyzed with account for the anisotropy of the thermal parameters and the permeability. For the Darcy–Boussinesq equations the conditions under which the problem pertains to the class of cosymmetric systems are established and explicit formulas for the critical Rayleigh numbers corresponding to the loss of stability of the mechanical equilibrium are derived. The critical numbers and the branching stationary convection regimes are calculated using a finite difference method conserving the problem cosymmetry.