Rayleigh Benard instabilities under high frequency vibration and magnetic field

We study the stability of an electrically conducting fluid layer contained between two rigid plates at different temperatures, subject to high-frequency vibration and to an external and constant magnetic field transverse with respect to the boundaries. Our purpose is to predict numerically the effect of such a magnetic field on the transition to instability under the combined action of heating and the high frequency vibrations. A particular attention is dedicated to the microgravity situation.