Non-darcy buoyancy flowin 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 TH was attained at the center of the bottom wall. The side walls were linearly heated, maintaining minimum temperature Tc at the top edges of the side walls and temperature Th at the bottom edges of the side walls; i.e, Tc ≤ Th ≤ TH. 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 = (Th - Tc)=(TH - Tc)(0 ≤ A ≤ 1) and Darcy number Da (10^-5 ≤ Da ≤ 10^-3) for higher Rayleigh number Ra = 10⁶ 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.