FINITE ELEMENT SIMULATIONS OF FREE CONVECTION FLOW INSIDE A POROUS INCLINED CAVITY FILLED WITH MICROPOLAR FLUID

Abstract

The present study predicts the effects of inclined magnetic field and thermal boundary conditions on the natural convection flow inside a porous conduit filled with micropolar fluid. The lower wall is cold and the inclined walls of the conduit are constantly or sinusoidally heated. The nonlinear partial differential equations are solved by employing a robust Galerkin finite element scheme. The pressure term in this scheme is eliminated by using a penalty method. The value of penalty parameter ∏ is set at 107 to ensure consistent solutions. The results are presented in the form of streamlines, temperature contours, and local and average Nusselt numbers. The results show that the magnitude of the stream function decreases with increasing the inclination angle of the applied magnetic field, Hartmann number, and micropolar parameter while an opposite trend is noted against Darcy number, Prandtl number, and inclination angle of cavity. The average Nusselt number is substantially higher for the uniform heated case in comparison to the sinusoidal heated case regardless of the choice of other physical parameters. Further, the average Nusselt numbers decrease by increasing micropolar parameter (R0) and Hartmann number (Ha) while an opposite trend prevails with increasing rest of the parameters (ω, Da, Pr) for both cases. It is noted that when the cavity is inclined at 45° or 90° and magnetic field is applied either along the x-axis (φ = 0°) or inclined at 45° or 90°, only clockwise circulation exists inside the conduit. The presence of counterclockwise circulating roll in the top corner of the cavity is linked with the choice of heating mode adopted at the side walls. In fact, such circulations are more likely to appear for the case of nonuniform heated side walls. The solution is benchmarked with the previous available data. The analysis presented here has potential application in solar collectors and porous heat exchanges.