Numerical Study of Oscillatory Natural Convection During Solidification of a Liquid Metal in a Rectangular Enclosure with and without Magnetic Field

Abstract

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.

The authors gratefully acknowledge the financial support of this work through Project J2501/03/57/06 provided by the Algerian Ministry of High Education and Scientific Research. The authors also take this opportunity to express sincere respect to the reviewers for their comments.