Free convection in a wavy cavity filled with heat-generating porous media

A numerical investigation of steady free convection inside a cavity made of two horizontal straight walls and two vertical wavy walls filled with a heat-generating porous medium is carried out. Wavy walls are assumed to follow the profile of a cosine curve. Horizontal straight walls are kept adiabatic, while the bent walls are isothermal and kept at the same temperature. The governing Darcy and energy equations were discretized using the Galerkin finite element method. The results provide detailed information on the influences of the governing parameters, which describe this problem. Simulations are carried out for a range of wave ratio 0 to 0.6, aspect ratio A 1 to 5, and Rayleigh number Ra 10 to 1000. Results are presented in the form of streamlines, isotherms, and local and average Nusselt numbers. Comparison with known results from the open literature for natural convection in a porous cavity with plane vertical walls ( 0) is in excellent agreement. In all the results presented, steady state has been attained.