Onset of convection in a porous layer with net through-flow and internal heat generation

Abstract

Onset of convection in a horizontal porous layer is investigated including the effects of through-flow and a uniformly distributed internal heat generation for different types of hydrodynamic boundary conditions. The instability parameter is either a Darcy-external or Darcy-internal Rayleigh number which has been determined numerically using Galerkin technique. When the boundary conditions at the top and bottom are not identical, it is found that a small amount of through-flow in one particular direction destabilizes the system in the absence of heat generation. However, in the presence of an internal heat generation, through-flow in one direction destabilizes the system even if the boundary conditions at the two boundaries are of the same type and the destabilization is found to be more with the increase in internal Rayleigh number.