Effect of Magnetic Field on Rayleigh Bénard Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid with Insulating Boundaries

The effect of the uniform vertical magnetic field acting opposite to gravity on the onset of steady Rayleigh-Bénard-Marangoni convection in horizontal layer of an electrically conducting liquid is investigated, using the modified linear stability theory. The upper surface of liquid layer is free where surface tension gradients arise on account of variation of temperature and the lower boundary surface is rigid, each subject to the constant heat flux condition. Both mechanisms namely, surface tension and buoyancy causing instability are taken into account. The Galerkin method is used to obtain the eigenvalue equation which is then computed numerically. Results of this analysis indicate that the critical eigenvalues in the presence of a uniform magnetic field are greater in a relatively hotter layer of liquid than a cooler one under identical conditions otherwise. The asymptotic behaviour of both the Rayleigh and Marangoni numbers for large values of the Chandrasekhar number is also obtained. During the course of this analysis, we also correct the inaccuracies in the work of earlier authors