Influence of Heat Sources and Thermal Boundary Conditions on Natural Convective Currents in a Trapezoidal Porous Cavity

This paper deals with steady laminar natural convective Darcian flow of a viscous incompressible fluid in a finite trapezoidal cavity filled with isotropic permeable material of low permeability. The vertical side walls of the cavity are assumed to be adiabatic, whereas the lower horizontal and the sloping upper walls are isothermal but with different temperatures. It is further assumed that the flow domain is subject to heat sources/sinks of uniform strength, resulting in the internal generation or absorption of heat. The governing non-dimensional partial differential equations, together with an appropriate set of thermal conditions and subject to Boussinesq approximation, have been solved numerically. The effects of a number of important non-dimensional quantities, namely Rayleigh–Darcy number, aspect ratio, internal heating parameter and inclination parameter have been discussed in relation to the isotherms and streamlines.