Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium

A theoretical analysis of incompressible magnetohydrodynamic (MHD) non-Darcian hydrogravitational convection in a square enclosure partially filled with a highly permeable medium in presence of transverse magnetic field is presented. A non-Darcy model is utilized for the porous region featuring both Darcian linear drag and second order Forchheimer drag components with Brinkman no-slip at the walls. The horizontal (i.e., bottom and Top) wall boundaries are considered adiabatic and impermeable, while the side walls (hot and cold walls) are maintained with different thermal values. The governing momenta and thermal conservation equations with appropriate end conditions are solved by Lattice Boltzmann method (LBM). A parametric examination of the impact of Hartmann number (0 < Ha < 50), Darcy number (0.0001 < Da < 0.1), and Rayleigh number (103 < Ra < 106) on temperature contours and streamline patterns for Helium gas (Prandtl number (Pr) = 0.71) is conducted. The heat flux distributions on the side walls and centre-line velocity are also computed. With greater Darcy number and Rayleigh number, Nusselt number is boosted at the left hot wall and the right cold wall. However, Nusselt number increases as one descends the hot wall toward the lower adiabatic boundary, and subsequently increases asone ascends the cold wall toward the upper adiabatic boundary.