Effect of anisotropy and boundary conditions on Darcy and Brinkman porous penetrative convection

Abstract We investigate the effects of anisotropic permeability and changing boundary conditions upon onset penetrative convection in a porous medium Darcy type Brinkman type. Attention is focussed on critical eigenfunctions which show how many cells will be found layer. The number shown to depend critically ratio vertical horizontal permeability, coefficient, upper condition for velocity may Dirichlet or constant pressure. Rayleigh numbers wave are determined, it an unconditional threshold nonlinear stability derived. Highlights Shows depends temperature layer anisotropy ceels coefficient patters ambient pressure