A boundary layer analysis of electro-magneto-hydrodynamic forced convective transport over a melting slab

In this work, a boundary layer based integral approach is employed for analyzing the coupled problem of electro-magneto-hydrodynamic convection and melting of an electrically conducting material. The melting process is assumed to occur on a semi-infinite flat horizontal slab. The simultaneous non-linear ordinary differential equations, originated out of the boundary layer analysis, are solved by employing the fourth order Runge–Kutta method, in a novel iterative framework. Simulation studies are executed for representative systems of materials, with a wide range of variation of processing parameters. Effects of melt superheat and the strengths of magnetic and electric fields on the melting process are analyzed in details. Fundamental physical principles are subsequently outlined for controlling the melting process through combined electrical and magnetic fields, on the employment of judicious combinations of the relevant operating parameters.