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.

Double Diffusive Natural Convection in Binary Mixture Under the Effect of External Magnetic Field: Steady and Oscillatory State

“…According to the methodology of the study of an oscillatory flow (unsteady) exposed to an external uniform magnetic field (Gelfgat and Yoeseph, [12]; Bessaï h and Bouabdallah, [13]; Bouabdallah and Bessaih, [14]; Ghernaout et al [15]), we consider in this study a magnetic field applied in two directions: horizontal (Bx) and vertical (By), and the Hartmann number varying from Ha = 0, 5, 10, 20, 30, 50 and 100. Whereas, for the molten metals and semi-conductors with the length scale of the cavity (L = 0.15 m), the applied magnetic field is of the order of 0.2 to 0.5 Tesla.…”

“…They showed that a vertical magnetic field provides a stronger stabilization effect, and also that the multiplicity of steady states is suppressed by the electromagnetic effect. During solidification of a pure metal Bessaï h and Bouabdallah [13] investigated numerically the two-dimensional oscillatory natural convection in a rectangular cavity subjected to an external and arbitrarily oriented magnetic field. The authors showed that the effect of a magnetic field with different orientations provides a notable change on the flow and thermal structures.…”

Effect of magnetic field on 3D flow and heat transfer during solidification from a melt

“…To employ the fixed grid, an enthalpy method is used to solve the phase change (Bessaïh and Bouabdallah, 2008). The liquid fraction expression in the solid phase, solid/liquid interface, and liquid phase, is given as: where L v represents the latent heat of fusion (for the gallium L v = 8.016 Â 10 4 J/kg).…”

“…In our previous work (Bessaïh and Bouabdallah, 2008), we have numerically investigated the two-dimensional oscillatory natural convection during solidification of a pure metal contained in a rectangular cavity, and subjected to an external and arbitrarily oriented magnetic field. We have showed that the effect of a magnetic field with different orientations provides a notable change on …”

Transient Laminar MHD Natural Convection Cooling in a Vertical Cylinder

“…Furthermore, the thermal stratification in the core is destroyed and the isotherms are parallel to the vertical walls. Bessaïh and Bouabdallah [11] investigated numerically the two-dimensional, oscillatory natural convection of a liquid metal solidification in a rectangular cavity in the presence of an external magnetic field. They showed that the vertical magnetic field stabilized the convection flow and they provided diagrams with dependencies of the critical Grashof numbers and frequencies on the magnetic field.…”