The effect of a magnetic field on the linear growth rates of Benard-Marangoni convection

We obtain explicit analytical expressions for the linear growth rates of the steady Benard-Marangoni convection in a horizontal layer of electrically-conducting fluid with a deformable free upper surface in the presence of a uniform vertical magnetic field subjected to a constant temperature at its lower boundary. The leading order behavior of the marginal stability curve for the onset of steady Benard-Marangoni convection is also given. The numerically-calculated linear growth rates showing the stabilizing effect of the magnetic field are presented.