Abstract
A thermal lattice Boltzmann model for incompressible flow is developed and extended to investigate the natural convection flow in porous media under the effect of uniform magnetic field. The study shows that the flow behaviour is various parameters dependent. The Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da) and the medium inclination angle from the horizontal (phi), the magnetic field orientation (psi) and the medium porosity (epsilon) effects are carried out in wide ranges encountered in industrial and engineering applications. It was found that the flow and temperature patterns change significantly when varying these parameters. To confirm the accuracy in present simulations, the present results are first validated on two test cases with and without magnetic field. A good agreement is observed by comparison with available previous works. It is found also that the lattice Boltzmann method is a reliable tool that gives a great deal of valuable information about the dynamics of buoyancy-driven flows and put on view the physics of the flow under stiff conditions.