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Analytical and numerical investigations were performed to study the influence of the Soret and Dufour effects on double-diffusive convection in a vertical porous layer filled with a binary mixture and subject to horizontal thermal and solute gradients. In particular, the study was focused on the effect of Soret and Dufour diffusion on bifurcation types from the rest state toward steady convective state, and then toward oscillatory convective state. The Brinkman-extended Darcy model and the Boussinesq approximation were employed to model the convective flow within the porous layer. Following past laboratory experiments, the investigations dealt with the particular situation where the solutal and thermal buoyancy forces were equal but acting in opposite direction to favor the possible occurrence of the rest state condition. For this situation, the onset of convection could be either supercritical or subcritical and occurred at given thresholds and following various bifurcation routes. The analytical investigation was based on the parallel flow approximation, which was valid only for a tall porous layer. A numerical linear stability analysis of the diffusive and convective states was performed on the basis of the finite element method. The thresholds of supercritical, RTCsup, and overstable, RTCover, convection were computed. In addition, the stability of the established convective flow, predicted by the parallel flow approximation, was studied numerically to predict the onset of Hopf’s bifurcation, RTCHopf, which marked the transition point from steady toward unsteady convective flows; a route towards the chaos. To support the analytical analyses of the convective flows and the numerical stability methodology and results, nonlinear numerical solutions of the full governing equations were obtained using a second-order finite difference method. Overall, the Soret and Dufour effects were seen to affect significantly the thresholds of stationary, overstable and oscillatory convection. The Hopf bifurcation was marked by secondary convective flows consisting of superposed vertical layers of opposite traveling waves. A good agreement was found between the predictions of the parallel flow approximation, the numerical solution and the linear stability results.

International audienceThis work presents a numerical study of natural convection in a laterally heated cavity filled with an electrically conductive fluid (Pr=0.0321) in the presence of an external magnetic field and an internal heat source. The finite volume method with the SIMPLER algorithm is used to solve the system of equations governing the magnetohydrodynamics flow. The influence of volumetric heating S-Q on the flow structure and on the heat transfer within the cavity for Gr=10(4), 10(5), and 10(6) was examined. The effects of aspect ratio (A=1, 0.5, and 2), Prandtl number (low Prandtl number fluids), and magnetic field (Ha=0 to 100) were determined in the steady state with internal heat generation. Two orientations of the magnetic field were considered in order to have better control of the flow. The strongest stabilization of the flow field with internal heat generation is found when the magnetic field is oriented horizontally