Effect of Uniform Magnetic Field on Rayleigh Bènard Marangoni Convection in a Relatively Hotter or Cooler Layer of Liquid

The effect of uniform vertical magnetic field on the onset of steady Rayleigh-Bènard-Marangoni convection in a relatively hotter or cooler layer of electrically conducting liquid is studied theoretically by means of modified linear stability analysis. The top surface of the layer is non-deformable free where surface tension gradients arise on account of variation of temperature, and the bottom surface is rigid and thermally conducting. The eigenvalue equation is obtained by using the Fourier series method. Numerical results are obtained and presented. The results of this analysis indicate that the critical eigenvalues in the presence of magnetic field are greater in a relatively hotter layer of liquid than a cooler one under identical conditions otherwise. A detail description of marginal stability curves showing the influence of the magnetic field is presented and discussed. The asymptotic behavior of the magnetic field for large values of Chandrasekhar number is also obtained.