Numerical study of oscillatory natural convection during solidification of a liquid metal in a rectangular enclosure with and without magnetic field

A numerical investigation of the two-dimensional, oscillatory natural convection during the solidification of a liquid metal contained in a rectangular cavity, having an aspect ratio equal to 4 and submitted to an external uniform magnetic field, is presented. The numerical approach is based on the finite-volume approximation with an enthalpy formulation. A computer program based on the SIMPLER algorithm is developed. The results show that the oscillatory flow in the liquid part of the enclosure appears by the formation of the principal and secondary cells, and periodic oscillations in the hydrodynamic and thermal fields. The effect of a magnetic field with different orientation provides a notable change on the flow and thermal structures. A discrete Fourier transform is used to determined the critical frequencies F-cr of oscillations. Stability diagrams show the dependence of the critical Grashof number Gr(cr) and the dimensionless critical frequency F-cr with the Hartmann number Ha. The strongest stabilization of the convection flow is found when the magnetic field is oriented vertically.