A comparative analysis of isotropic and anisotropic features on natural convection in a permeable cavity

The natural convection process occurring in finite cavities is a subject of great research interest in many technological applications. When the cavity has 4-sided walls, the thermal conditions prevailing on these boundaries play significant roles on the flow and thermal characteristics. There are a number of applications where the thermal wall conditions are typically adiabatic on the side vertical walls while the lower and upper walls are isothermal with different temperatures. Moreover, depending upon the nature of applications, one has to consider the isotropic or anisotropic features of the hydrodynamical and thermal characteristics of the porous material. This paper deals with steady laminar natural convective Darcian flow of a viscous incompressible fluid in a finite trapezoidal cavity whose side walls are vertical and the upper wall is slanted. The vertical side walls of the cavity are assumed to be subject to no heat flux condition while the remaining walls are kept at uniform temperatures. We have solved numerically the governing non-dimensional partial differential equations together with the appropriate sets of boundary conditions for velocity and temperature. In order to bring out the salient features of non-isotropy versus isotropy, the effects of a number of important non-dimensional quantities, namely, Rayleigh-Darcy number, aspect ratio, inclination parameter, permeability ratio and thermal diffusivity ratio parameters have been discussed in relation to the streamlines and isotherms.