The effect of a uniform magnetic field on the onset of steady Marangoni convection in a layer of conducting fluid with a prescribed heat flux at its lower boundary

Abstract

In this paper a combination of analytical and numerical techniques are used to analyze the effect of a uniform vertical magnetic field on the onset of steady Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid with a uniform vertical temperature gradient subject to a prescribed heat flux at its rigid lower boundary. Critical Marangoni numbers for the onset of instability are calculated which are significantly different from those calculated previously in the case of an isothermal lower boundary. Analytical results for the behavior of the critical Marangoni number in the asymptotic limit of large magnetic field strength are also obtained. It is concluded that the magnetic field always has a stabilizing effect on the onset of steady Marangoni convection, but that when the free surface is deformable situations with a sufficiently large Marangoni number will always have unstable modes no matter how strong the applied magnetic field is.