Abstract

The present paper reports on an analytical and numerical study of combined Soret and Dufour effects on thermosolutal convection in a horizontal porous cavity saturated with an electrically conducting binary fluid under a magnetic field. The horizontal walls of the system are subject to vertical uniform fluxes of heat and mass, whereas the vertical walls are assumed to be adiabatic and impermeable. The main governing parameters of the problem are the Rayleigh, the Hartmann, the Soret, the Dufour and the Lewis numbers, the buoyancy ratio, the enclosure aspect ratio, and the normalized porosity of the porous medium. An asymptotic parallel flow approximation is applied to determine the onset of subcritical nonlinear convection. In addition, a linear stability analysis is performed to predict explicitly the thresholds for the onset of stationary, overstable and oscillatory convection, and the Hopf bifurcation as functions of the governing parameters. The combined effect of a magnetic field, Soret and Dufour parameters have a noticeable influence on the intensity of the convective flow, the heat and mass transfer rates, and the thresholds of linear convection. It is found that the imposition of a magnetic field delays the onset of convection and its intensification can lead to the total suppression of the convective currents. The heat transfer rate increases with the Dufour number and decreases with the Soret number and vice versa for the mass transfer rate.

Highlights

  • The problem of thermosolutal natural convection in enclosures filled with saturated porous media with or without the presence of a magnetic field had been the subject of numerous recent and past studies

  • The authors showed that the permeability of the two porous layers and the variation of the ratios of thermal conductivities and mass diffusivities had a significant influence on the double diffusive convection, the flow structure, and on the heat and mass transfer rates

  • The results indicated that, for aiding flows, the local Nusselt number increased with increasing the power–law index and the Soret number or decreased with the radiation parameter and the Dufour number

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Summary

Introduction

The problem of thermosolutal natural convection in enclosures filled with saturated porous media with or without the presence of a magnetic field had been the subject of numerous recent and past studies. In most if not all of the past studies on thermosolutal convection in porous enclosures, based on the above literature survey, the Soret and Dufour effects under the influence of a magnetic field on the unsteady double diffusive natural convection and the determination of the thresholds for the onset of subcritical, oscillatory, and stationary convections have not been addressed yet. The present investigation focuses on the examination of the combined effects of Soret and Dufour with the presence of a magnetic field on the unsteady double diffusive natural convection, and on the structure and intensity of the convective flow, and on the heat and mass transfer characteristics inside a horizontal rectangular enclosure saturated with an electrically conducting binary mixture. A whole picture is drawn about various convection modes from rest state to unsteady convection modes within their delineated regions of existence

Geometry and Governing Equation
The physical model and coordinate
Numerical Solutions
Analytical Solution
Stability Analysis
Stability of the Rest State
Stability of the Convective State
Results and Discussion
Subcritical
Full Text
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