Conjugate natural convection in a porous enclosure: effect of conduction in one of the vertical walls

Steady conjugate natural convection–conduction heat transfer in a two-dimensional porous enclosure with finite wall thickness is studied numerically in the present article. The horizontal heating is considered, where the vertical boundaries are isothermal at different temperatures with adiabatic horizontal boundaries. The Darcy model is used in the mathematical formulation for the porous layer and finite volume method is used to solve the dimensionless governing equations. The governing parameters considered are the Rayleigh number (10⩽Ra⩽1000), the wall to porous thermal conductivity ratio (0.1⩽Kr⩽10) and the ratio of wall thickness to its height (0.02⩽D⩽0.5). The results are presented to show the effect of these parameters on the heat transfer and fluid flow characteristics. The results including the streamlines and isotherm patterns and the local and average Nusselt number for different values of the governing parameters. It is found, in most of the cases that either increasing the Rayleigh number and the thermal conductivity ratio or decreasing the thickness of the bounded wall can increase the average Nusselt number for the porous enclosure (). In special cases at low Ra and high conductive walls, the values of are increasing with the increase of the wall thickness.