Lattice Boltzmann simulation of thermo-magnetic natural convection in an enclosure partially filled with a porous medium
K. Venkatadri, O. Anwar Bég
Abstract
Motivated by emerging magnetized hybrid fuel cell applications, a theoretical analysis \nof incompressible magnetohydrodynamic (MHD) non-Darcian thermogravitational convection \nin a square enclosure partially filled with a highly permeable medium in presence of transverse \nmagnetic field is presented. The enclosure is filled with magnetized Newtonian fluid. A nonDarcy model is utilized for the porous region featuring both Darcian linear drag and second \norder Forchheimer drag components with Brinkman no-slip at the walls. The horizontal (i.e., \nbottom and Top) wall boundaries are considered adibatic and impermeable, while the side walls \n(hot and cold walls) are maintained with different thermal values. The Lattice Boltzmann \nmethod (LBM) is implemented to employ the governing momenta and thermal conservation \nequations with appropriate end conditions. The divergence of the non-linear system is avoided \nby introducing convergence criteria factors. A grid independence test is included for validation \nof the D2Q9-LBM code accuracy. Further validation with earlier studies in the absence of \nHartmann number (Ha) is included. A parametric examination of the impact of Hartmann \nnumber (0 < Ha < 50), Darcy number (0.0001 < Da < 0.1), and Rayleigh number (103 < Ra < \n106 \n) on temperature contours and streamline patterns for Helium gas (Prandtl number (Pr) = \n0.71) is conducted. The heat flux distributions on the side walls and centre-line velocity are \nalso computed. With greater Darcy number and Rayleigh number, Nusselt number is boosted \nat the left hot wall and the right cold wall. However, Nusselt number increases as one descends the hot wall towards the lower adiabatic boundary whereas for it increases as one ascends the \ncold wall towards the upper adiabatic boundary.