Three-dimensional numerical modeling of free convection in sloping porous enclosures

Three-dimensional (3D) numerical simulations are carried out to study steady state free convection in a sloping porous enclosure heated from below. The model is based on Darcy's law and the Boussinesq approximation. Two different approaches to solve this problem are compared: primitive variables and vector potential. Although both numerical models lead to equivalent results in terms of the Nusselt number and convective modes, the vector potential model proved to be less mesh-dependent and also a faster algorithm. A parametric study of the problem considering Rayleigh number, slope angle and aspect ratio showed that convective modes with irregular 3D geometries can develop in a wide variety of situations, including horizontal porous enclosure at relatively low Rayleigh numbers. The convective modes that have been described in previous 2D studies (multicellular and single cell) are also present in the 3D case. Nonetheless the results presented here show that the transition between these convective modes follows an irregular 3D geometry characterized by the interaction of transverse and longitudinal coils.