Numerical Investigation of MHD Natural Convection Flow in Porous Media: A Comparative Study of Cavity Geometry Shapes

In the current study, we considered a 2D enclosed porous media in three cases: rectangular, rectangular with chamfer corners, and pentagon with variable hollows. The impact of three cavity shapes, including triangle, rectangle, and lozenge shapes, on the Nusselt number at the local state, vertical velocity, total entropy, horizontal velocity, and isotherm of the porous enclosure is analyzed. The finite element method (FEM) is used to solve governing equations for fluid flow and heat transfer in a saturated non-Darcy porous medium with dissipation influences and radiation, subject to corresponding boundary conditions. In this work, we presented the pentagonal porous media shape (Case 3) as a novelty. The impact of the dimensionless parameters, such as Eckert number, on velocity profiles and temperature distribution is discussed for nine modes of different porous media geometries with varied hollows. The essential dimensionless parameters have been simulated by employing the following ranges: radiation parameter (0.5 Rd 5), Eckert number (10^(-6) Ec 3×10^(-5)), Rayleigh number (5×10^4 Ra 10^5), and Prandtl number (0.7 Pr 1). The presented numerical simulation shows excellent agreement with the results from the previous research. Based on the simulation results, the regions exhibiting the most entropy generation are the base of the hot side and the upper surface of the cavity. In addition, case 3 is accompanied by the Nusselt number at local state improvement and reduction in fluid vertical and horizontal velocities. The results show that an increase in Eckert number in Case 3 with varied hollow leads to a corresponding increase in vertical velocity.