In this numerical simulation, we have studied the natural convection of air under the influence of a magnetic field of Hartmann number Ha = 0.1 for a value of the Rayleigh number Ra = 104. The air fluid is confined between two rectangular parallelepipeds of square straight sections whose internal cavity is subjected to a heat flow of constant density and the external cavity is at constant temperature. We have applied the vorticity current function formalism to get rid of the pressure gradient in the equation of motion because the fundamental element of natural convection is the Rayleigh number. Without a magnetic field, we notice, for isothermal lines, a loosening of cells and formation of a peak in the middle of the upper internal cavity while for current lines, we have two cellular areas of opposite direction that tend to approach towards the middle of the cavity. As soon as the magnetic field is applied for a Hartmann number Ha = 0.1, we will see thermal and dynamic changes causing the formation of four recirculation zones for the current lines and a standardization of the temperature for the isotherms. To see the interaction between the wall and the fluid, we have studied the behavior of parietal quantities such as the Nusselt number and the coefficient of friction.

Keywords : Ansys Fluent; Convection; Finite Volume; Magnetic Field.