Digital resolution of the system of governing equations of the natural magnetohydrodynamic convection phenomenon

In this study, hydrodynamic and magnetic anisotropiesas buoyancy-driven convection effects in a two-dimensional horizontal cavity are investigated analytically. The porous cavity filled with a porous medium is heated isothermally by the sides and its horizontal walls are thermally insulated or conducted gold. The main directions of permeability are oriented in the direction of that is oblique to gravity. Based on scale analysis, solutions for the flow field, temperature distribution, and Nusselt number are obtained. The limiting case corresponding to pure fluid media, and pure porous media, complete these results in order to validate them when compared to those obtained in the literature. It is found that temperature and velocity fields are modified significantlywhen applying the transverse magnetic field. Also, the effects of anisotropic parameters on heat transfer are strongly significant.