Buoyancy and thermocapillary driven convection flow of an electrically conducting fluid in an enclosure with heat generation

The effect of surface tension on unsteady laminar natural convection flow of an electrically conducting fluid in a rectangular enclosure under an externally imposed magnetic field with internal heat generation has been investigated. The top horizontal surface of the rectangular cavity is assumed to be free and the bottom one insulated, whereas the left vertical wall is cold and the right one is uniformly hot. The equations are non-dimensionalized and solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of heat generation together with the combined effects of the magnetic field and the surface tension are presented graphically in terms of isotherm and streamline plots. The effects of varying the physical parameters on the rate of heat transfer from the heated surface of the enclosure are also depicted. The fluid here has Prandtl number Pr=0.054 which is representative of liquid metal and semiconductor melts.