Thermo-Solutal Convection Modelling during the Directional Solidification Process of an Electrically Conducting Binary Alloy in the Presence and without a Magnetic Field

F. Mechighel and M. Kadja (Algeria)


Thermo-solutal convection, directional solidification, continuum model, magnetic field, binary alloy


A mathematical model, based on continuum model of two-phase flow of convection, for numerically simulating of thermo-solutal convection during directional solidification process of a binary alloy is presented. Firstly, the simulation has been performed without magnetic field and secondly it has been performed in an applied magnetic field. The model includes mass, momentum, energy and species conservation equations written in compressible form. These equations have been written in non-dimensional form in order to introduce dimensionless numbers. The geometry under study is rectangular. The macroscale transport in the solidification of alloy is governed by the progress of the two-phase mushy zone which is treated by using the equation of Blake-Kozeny. The system of equation written has been discretized by means of finite volume method. For solution of discretized equations the SIMPLER algorithm together with Thomas algorithm are used. Temperature and mass fraction solid are calculated from the continuum enthalpy and concentration. The effect of the magnetic field on the solidification is studied. The simulation results show good agreement qualitatively with the experimental observations reported in related literatures.

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