Comparison of criterional estimates and numerical calculations of the magnetic field effect on the heat and mass transfer in melts under microgravity conditions

It is of interest to analyze the simultaneous effects of the microgravitational condition and a constant magnetic field on the conceive processes in a rather common technological experiment, namely the crucible-free melt zone (FMZ). The convective flow features in this case are, first of all, small Grashof numbers in the case of a gravitational type convection, and secondly, the dominant role of the thermocapillary convection in the presence of free nonisothermal liquid surfaces. A question arises concerning the scale estimates which characterize the magnetic field effect on convection under these conditions, and about their applicability to an approximate analysis of the effectiveness of the field action. To answer this question, we discuss the system of the Navier-Stokes equations, taking account the electromagnetic force.