Interaction of Kelvin force and transport across a melting substrate in a microgravity environment

Gradients in magnetic field applied to electrically insulating fluids result in an effective body force-the Kelvin force, which can potentially be used to control flow and thermal processes, particularly in microgravity environments. We study the influence of the Kelvin force on the mass, momentum, and energy transport of fluid arising from the melting of a semi-infinite solid substrate subjected to temperature and magnetic-field gradients. The governing equations of the magnetothermal free convection of the melt under the boundary layer approximation with a suitable transformation lead to a similarity solution. Closed-form analytical solutions for the limiting case of smaller Prandtl numbers are presented. The nonlinear similarity equations are solved numerically using an iterative boundary-value technique based on a finite-difference approach. Based on the numerical results, the effect of various characteristic nondimensional parameters on the structure of the melt boundary layer and transport rates of heat and mass across the substrate are elucidated and discussed.