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

Ismail Filahi,Mohamed Bourich,Mohammed Hasnaoui,Abdelkhalek Amahmid

doi:10.1155/2020/4046570

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.

Highlights

Natural convection involving binary mixtures in the porous and fluid media is still a relevant field of investigation since it occurs in wide ranges of applications in many engineering problems and natural fields such as geophysics, oil reservoirs, storage of nuclear wastes, operation of solar ponds, chemical reactors, migration of mixtures in fibrous insulation, and metal manufacturing processes. is phenomenon occurs due to temperature differences, concentration differences, or by combination of these two differences [1]
Convection in which the buoyancy forces are due to both temperature and chemical concentration gradients is referred to as thermosolutal or double-diffusive convection
Mathematical Problems in Engineering thresholds [17], reversal of the horizontal concentration gradient [18], and a comparison study between the cases where the enclosure is filled with a clear binary mixture or a saturated porous medium [19]

Summary

Introduction

Natural convection involving binary mixtures in the porous and fluid media is still a relevant field of investigation since it occurs in wide ranges of applications in many engineering problems and natural fields such as geophysics, oil reservoirs, storage of nuclear wastes, operation of solar ponds, chemical reactors, migration of mixtures in fibrous insulation, and metal manufacturing processes. is phenomenon occurs due to temperature differences, concentration differences, or by combination of these two differences [1]. Balla and Naikoti [28] analyzed numerically double-diffusive free convection heat and solute transfer in an inclined square porous cavity saturated with a fluid in the presence of Soret and Dufour effects. E main objective is to bring out the combined effects of Soret and Dufour parameters on thresholds of convection, fluid flow, and heat and mass transfer characteristics.

Results

Conclusion