Influence of anisotropy on convection in porous media with nonuniform thermal gradient

Effect of anisotropy on the onset of natural convection heat transfer in a fluid saturated porous horizontal cavity subjected to nonuniform thermal gradients is investigated analytically. The porous layer is heated from the bottom by a constant heat flux while the other surfaces are being insulated. The horizontal boundaries are either rigid/rigid or stress-free/stress-free. The hydrodynamic anisotropy of the porous matrix is considered. The principal directions of the permeability are oriented in a direction that is oblique to the gravity. Based on a parallel flow assumption, closed-form solution for the flow and heat transfer variables, valid for the onset of convection corresponding to vanishingly small wave number, is obtained in terms of the Darcy–Rayleigh number Ra, the Darcy number Da, and the anisotropic parameters K * and θ. The critical Rayleigh number for the onset of convection arising from sudden heating and cooling at the boundaries is also predicted. The limiting cases Da→∞ (for a viscous pure fluid) and Da→0 (for anisotropic porous media) completed all results. It is demonstrated that effects of anisotropic parameters are strongly significant.