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In this paper, double diffusive natural convection in binary mixture under the effect of external magnetic field for the steady and the oscillatory state is numerically investigated. For this end, a square cavity filled with a binary mixture has been considered; the cavity is exposed to opposing solute and thermal gradients. An external uniform magnetic field is applied separately in two directions (i.e. horizontal and vertical). The following flow parameters were considered: Prandtl number Pr = 0.71, Schmidt number Sc = 3.5 and buoyancy ratio N = 0.75, 1.0, and 1.25. The finite volume method with SIMPLER Algorithm was used to solve numerically the mathematical model. The model was validated and showed good agreement with experimental results of the literature. The obtained results showed a strong dependence of the structure of thermal and solutal effect to the buoyancy ratio. The oscillatory double diffusive flow occurs for a periodic time where the phenomenon change around in each period time. A critical thermal Rayleigh number RaTCr and corresponding dominated frequency for the onset of oscillatory double diffusive convection were determined for each N and for different values of Hartman number (0, 25, 50, and 100).

A numerical study of Rayleigh-Bé nard convection in a rectangular cavity has been presented. The onset of natural convection and the transition from laminar to oscillatory convection were considered in this study. The finite volume method was used to solve numerically the governing equations of the phenomenon and the pressure-velocity coupling was matched by SIMPLER Algorithm of Patankar. This study was carried out for Rayleigh number varied from 10 3 to 10 6 in order to control the first value of critical Rayleigh number, Rac-1 corresponding the onset of convection, and that for different aspect ratios of the cavity. The threshold transition regime of laminar-oscillatory convection is depicted by the second critical Rayleigh number Rac-2. Also, the different modes of bifurcation of convection were determined and discussed.

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