Conjugate natural convection in a square enclosure under horizontal magnetic field effect

Steady, laminar, conjugate natural convection flow in a square enclosure is considered. Both effects: conduction in a vertical wall and the presence of a magnetic field are taken together. The enclosure is filled with liquid gallium and subjected to horizontal temperature gradient. The main focus of the study is examining the effect of Hartmann number on fluid flow and heat transfer. The effect of Rayleigh number and conduction in the left wall is also considered. The obtained result show in the absence of a magnetic field that natural convection can be strengthed by the increase of both Rayleigh number and conductivity ratio, because of the increase of the effective temperature difference driving the flow. For poor conducting wall, where the solid part is an insulated material and the thermal resistance is more important the average Nusselt number is approximately constant and having low values comparing with equal and high conducting wall, indicating that most of heat transfer is by heat conduction. In the presence of a magnetic field the results show that for a given Rayleigh number, as the value of Hartmann number increases, convection is suppressed progressively and the rate of heat transfer is reduced in the enclosure.