NON-DARCY BUOYANCY FLOW IN A SQUARE CAVITY FILLED WITH POROUS MEDIUM FOR VARIOUS TEMPERATURE DIFFERENCE ASPECT RATIOS

A finite element analysis has been carried out to study the influence of a sinusoidally heated bottom wall and linearly heated side walls on natural convection flows in a square cavity filled with a porous medium when the top wall is well insulated. The Darcy-Forchheimer model without the inertia term is used to predict the temperature and flow circulations in the porous medium. In the present study, for a non-uniformly heated bottom wall, the maximum temperature T-H was attained at the center of the bottom wall. The side walls were linearly heated, maintaining minimum temperature T-c at the top edges of the side walls and temperature T-h at the bottom edges of the side walls; i.e, T-c <= T-h <= T-H. The penalty finite-element method with bi-quadratic rectangular elements was used to solve the non-dimensional governing equations for coupled thermal and flow fields. Numerical results are presented for a wide range of parameters of temperature difference aspect ratio A = (T-h - T-c)/(T-H - T-c)(0 <= A <= 1) and Darcy number Da (10(-5) <= Da <= 10(-3)) for higher Rayleigh number Ra = 10(6) and Prandtl number Pr = 0.7 in terms of stream functions and isotherm contours. Furthermore, the effect of the temperature difference aspect ratio on local and average Nusselt numbers has been analyzed.