Free convection along a vertical heated plate in a porous medium with anisotropic permeability

Natural convection from a semi‐infinite vertical plate embedded in a fluid saturated porous medium is studied both analytically and numerically. The plate is assumed to be heated isothermally or by a constant heat flux. The porous medium, modeled according to Darcy’s law, is anisotropic in permeability with its principal axes oriented in a direction that is oblique to the gravity vector. In the large Rayleigh number limit, the governing boundary‐layer equations are solved in closed form, using a similarity transformation. Comparisons between the numerical solution of the full equations and analytical solutions are presented for a wide range of the governing parameters. The effects of the anisotropic permeability ratio K^*, of the orientation angle of the principal axes θ, and of the Rayleigh number R_H on the flow and heat transfer are investigated. Results indicate that the anisotropic properties of the porous medium considerably modify the heat transfer, velocity and temperature profiles from that expected under isotropic conditions.