Asian Journal of Pure and Applied Mathematics

The effect of the uniform vertical magnetic field acting opposite to gravity on the onset of steady Rayleigh-Bnard-Marangoni convection in horizontal layer of an electrically conducting liquid is investigated, using the modied linear stability theory. The upper and lower surface of liquid layer are free, each subject to the constant heat ux 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 eld 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.