Convection of electrically conducting fluids such as liquid metals in the presence of magnetic field is a major area of investigation, e.g., crystal growth processes. The usage of a magnetic field is known to inhibit the thermal flow in the liquidus phase, and it is utilized in the design phase of casting systems. This study is concerned with the heat transfer and flow in electro-conductive melts in solidification systems. A mathematical model of the underlying physical processes is established, and numerical simulation results obtained by a home-made code, based on the finite differences HSMAC scheme, are reported: second order central finite differences for the viscous terms, third order upwind (UTOPIA) finite differences for the convective terms, and first order forward finite differences for the time derivative.

Keywords: Electroconductive fluids, Convection heat transfer, Numerical simulation, Highly simplified mark and cell (HSMAC).