Natural convection in a cavity with a sloping upper surface filled with an anisotropic porous material

Steady natural convection in a viscous incompressible fluid flowing in a vertical permeable non-rectangular cavity is considered. The permeability of the porous medium and the thermal diffusivity of the fluid are assumed to be anisotropic in nature. Using the Boussinesq approximation and the Darcy law to model the porous medium, the governing equations-recast in terms of a stream function-are solved numerically. An algebraic grid generation technique is employed to transform the non-rectangular domain to a square domain. The influence of a number of parameters, arising due to geometrical and physical aspects, is discussed in relation to the flow and heat transfer.