Analytical and Numerical Study of Soret and Dufour Effects on Thermosolutal Convection in a Horizontal Brinkman Porous Layer with a Stress-Free Upper Boundary

Abstract

In this paper, thermo-diffusion (Soret effect) and diffusion-thermo (Dufour effect) effects on double-diffusive natural convection induced in a horizontal Brinkman porous layer with a stress-free upper boundary are investigated. The cavity is filled with a binary fluid and subjected to uniform fluxes of heat and mass on its long sides. An analytical solution based on the parallel flow approximation is developed for the problem considered in order to allow prompt determination of the thresholds of stationary and finite amplitude solutions and also heat and mass transfer characteristics. The analytical solution is validated numerically by using a finite difference method. The combined effects of the Soret and Dufour parameters, the thermal Rayleigh number, the buoyancy ratio, and the Darcy number on the flow intensity and heat and mass transfer are illustrated graphically, and some particular behaviors observed are discussed. The analytical solution proves the existence of different regions in the buoyancy ratio-Dufour parameter plane, corresponding to different parallel flow behaviors. The number, the location, and the extent of these regions, which are impossible to predict numerically, depend strongly on Soret and Dufour parameters. The effect of thermo-diffusion and diffusion-thermo on flow intensity and heat and mass transfer is found to be important.

Soret and Dufour effects on thresholds of stability in a horizontal Brinkman porous layer submitted to vertical temperature and species gradients using linear and non-linear analysis

“…In fact, the zones 1, 2, and 6 exist only when N/Le≤−1 and the existence of the zones 3, 4 and 5 is conditioned by the satisfaction of the inequality N/Le>−1. Details concerning the analytical procedure leading to the determination of these zones are given in the reference 36 . An illustration of the zones obtained in the (Du, Sr) plane is exemplified in Figure 11 for Le=1.1, Da=0.01 and N=2 and −2.

Figure 11.Zones delineating different flow behaviors for (a) N = −2 and (b) N = 2.

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“…34 It should be also mentioned that the threshold for subcritical convection, R sub TC , cannot be deduced from the linear stability analysis as the latter mode starts with a finite amplitude (but not with infinitesimal amplitude) perturbation. In this study, its expression given by equation (36) was deduced from the parallel flow approximation which takes into account the non-linearity, provided that the porous layer aspect ratio is large enough to allow the existence of such flow.…”

Linear and Nonlinear Stability Analyses of Double-Diffusive Convection in a Vertical Brinkman Porous Enclosure under Soret and Dufour Effects

“…The influence of the governing parameters on the resulting fluid flow, temperature, and concentration fields was discussed in details. More recently, Lagra et al [48], Attia et al [49], and Hasnaoui et al [50] investigated analytically and numerically the Soret and Dufour effects on thermosolutal convection induced in a horizontal layer subject to constant heat and mass fluxes. The influence of the Soret and Dufour effects on the thresholds of stationary convection, subcritical convection, flow structure, and heat and mass transfer rates were discussed.…”