Natural convection driven by buoyancy and surface tension forces under external magnetic field

Two-dimensional natural convection driven both by buoyancy and surface tension in the horizontal layer of an electrically conducting liquid which is subjected to a horizontal temperature gradient and a vertical magnetic field is studied theoretically. The flow and temperature distribution in the liquid layer is analysed for two cases; (1) the top surface is free and the bottom is a rigid wall, and (2) both surfaces are rigid. The effect of the magnetic field on the flow velocity and the temperature distribution is made clear and the simple expressions are obtained for two extreme cases of the sufficiently large magnetic field and the small magnetic field.