In this paper we have done the numerical study of the magneto thermal convection of air in a rectangular enclosure. We use the finite volume method to solve numerically the dimensionless Navier-Stokes equations that govern our flow. This resolution goes through the sequences of the SIMPLER algorithm which summarizes the different calculation steps. An essential part of the literature in the field is in agreement with the results of our numerical simulation. Indeed, it is shown that the longer the calculation time, the more the effects were visible on the velocity profile as well as those of the isotherms in the fluid domain. Similarly, the parallel orientation of the magnetic field with respect to the flow favored an increase in the velocity in the direction of flow due to the presence of the magnetic force. The representation of variations in the Nusselt number shows that it varies in opposite directions with the increase in temperature near heated walls.
