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.

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In this work, a numerical study of double-diffusive convection in binary mixture has been presented. A square cavity filled with a binary mixture and exposed to opposition solute and thermal gradients has been considered. The following flow parameters were considered: Prandtl number Pr ¼ 10, Lewis number Le ¼ 10, and buoyancy ratio varies 0 N 2. The finite volume method with SIMPLER algorithm was used to solving numerically the mathematical model. Our computer code is validated and shows a good agreement with literature available results. The obtained results show a strongest dependence of the thermal structure and solute effect with the buoyancy ratio. The oscillatory double-diffusive flow appeared from periodic time-evolution where the phenomena retuned in each period time. A critical thermal Rayleigh number Ra Tcr and corresponding dominated frequency for the onset of oscillatory double-diffusive convection were determined for each buoyancy ratio N, and the results show a strongest dependence between the buoyancy ratio and critical Rayleigh number. Also, the dominance of solute force increases the intensity of the flow better than the case of the dominance of thermal force.