Mathematical modelling of frequency and force impacts on averaged metal flows in alternating magnetic field

•The convection of metal in alternating magnetic field is studied.•Significant buoyancy impact on forced convection for frequency range was found.•Maps of quasi-steady averaged flows was plotted in plane frequency-force parameters.•The frequency dependence of loss sensitivity to properties was found. The averaged quasi-steady flow patterns of metal melt situated in alternating magnetic field are studied numerically. It is taken into account the buoyancy due to non-uniform heating, the intensive radiation heatsink from the melt surface and the Lorentz forces arising in conductor in the alternating magnetic field. The governing equations of the suggested mathematical model are given and the model validations are described. The flow regime maps are plotted based on analysis of melt velocity dependence on the Hartmann number and the parameter of magnetic field diffusion. Flow patterns corresponding each parameter area at the map are given and interpreted. The way of acceleration of melt motion computation is suggested.