Natural convection in a vertical slot filled with an anisotropic porous medium with oblique principal axes

Natural convection heat transfer in a rectangular cavity filled with a saturated anisotropic porous medium is investigated analytically and numerically. The side walls of the cavity are heated and cooled isothermally, while the horizontal walls are adiabatic. The porous medium 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 a boundary layer solution, based on the integral relations approach developed by Simpkins and Blythe [17], is proposed. Scale analysis is applied to predict the order of magnitudes involved in the boundary layer regime. Comparisons between the numerical solution of the full equations and analytical solutions are presented for a wide range of the governing parameters. The numerical experiments confirm the flow features and scales anticipated by the approximate boundary layer solution. It is demonstrated that the anisotropic properties and different orientation of the porous medium considerably modify the flow pattern and heat transfer rate from that expected under isotropic conditions.