Steady free convection in an anisotropic porous non-rectangular vertical cavity

Free convection in a porous non-rectangular vertical cavity with a sloping upper boundary has been considered. It is assumed that the cavity is filled with porous material subject to hydrodynamical and thermal anisotropy. Assuming Darcy law to hold, together with Boussinesq approximation, the governing partial differential equations have been solved numerically. To facilitate the computation, the non-rectangular physical domain has been transformed to a square computational domain using an algebraic grid generation method. The effect of a range of parameters of interest such as slope of the upper boundary, Darcy-Rayleigh number and aspect ratio, has been illustrated through plots of streamlines and isotherms. Furthermore, the variation of the average Nusselt number has also been discussed in relation to the anisotropic parameters and inclination of the upper surface.