Effects of magnetic field and buoyancy on onset of Marangoni convection

The onset of Marangoni convection in an electrically conducting liquid layer is studied theoretically for the case that the liquid is subjected to a vertical temperature gradient and a magnetic field. The effects of the intensity of magnetic field, the Biot number at the free surface, and the buoyancy on the critical Marangoni number and the flow patterns are shown. It is found that the onset of Marangoni convection is suppressed under the magnetic field and that the distance between each cell which is generated at a critical condition becomes shorter as the intensity of magnetic field increases. The relation between the critical Marangoni number and the Rayleigh number is expressed by Ma/Mac + Ra/Rac = 1.