Magneto-convective flow in a differentially heated enclosure containing a non-Darcy porous medium with thermal radiation effects: a lattice Boltzmann simulation

A computational study is presented for the impact of thermal radiation on incompressible magnetohydrodynamic (MHD) free convection within a square-shaped enclosure that is differentially heated and contains a non-Darcian porous medium saturated with an electrically conducting fluid. The Rosseland algebraic flux model is used to simulate radiative heat transport. The mass, momentum, and energy conservation equations, along with the corresponding boundary conditions, have been transformed into non-dimensional forms. The emerging dimensionless nonlinear boundary value problem is solved with the D2Q9-based lattice Boltzmann method. The main objectives are to determine the effects of Hartmann number, thermal radiation parameter, Darcy number, and Rayleigh number on the thermofluid characteristics for ionized hydrogen gas (Prandtl number, P \(r=0.69\)) in terms of the distributions of isotherms and streamlines. D2Q9-LBM code accuracy has been validated using a grid independence test. The current research’s findings are pertinent to the simulation of hybrid ionised MHD fuel cells and the production of magnetic materials.