Soret effect on double-diffusive multiple solutions in a square porous cavity subject to cross gradients of temperature and concentration

Mansour, A.; Amahmid, A.; Hasnaoui, M.; Bourich, M.

doi:10.1016/j.icheatmasstransfer.2004.02.013

Cited by 18 publications

(4 citation statements)

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“…The multiplicity of solutions was also proved for sufficiently small values of N (case of dominating thermal buoyancy forces) and the induced heat and mass transfer were found to be highly dependent on the considered solution in the ranges of parameters where multiple steady states are possible. The existence of multiple steady-state solutions, induced by doublediffusive convection in the presence of Soret effect was also reported in the literature in the case of a square porous cavity submitted to cross gradients of temperature and concentration by Bennacer et al [25] and Mansour et al [26]. The latter reported that, depending on the Soret parameter value, one to three convective solutions were found to be possible.…”

Section: Introductionsupporting

confidence: 56%

“…It should be noted that under 2D approach, the multiplicity of solutions is also possible in the steady regime and it is characterized by the existence of monocellular with clockwise or trigonometric flows, bicellular natural or anti-natural flows, and tricellular flows with a clockwise (or trigonometric) central cell and trigonometric (or clockwise) lateral cells. Note that the multiplicity of solutions, characterized by the existence of monocellular, bicellular [21,23,24,26,27] and tricellular [27] flows, was reported in several previous studies for square porous cavities using 2D approaches under different boundary conditions. In the following sections, we analyze the effect of the controlling parameters which are the Rayleigh number, Ra and the buoyancy ratio, N on the existence ranges of the multiple steady-state solutions developed in a cubical porous medium.…”

Section: Resultsmentioning

confidence: 65%

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Two- and three-dimensional multiple steady states in a porous cavity heated and salted from below

Khadiri

Bennacer

Hasnaoui

et al. 2011

International Journal of Thermal Sciences

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Section: Introductionsupporting

confidence: 56%

Section: Resultsmentioning

confidence: 65%

Two- and three-dimensional multiple steady states in a porous cavity heated and salted from below

Khadiri

Bennacer

Hasnaoui

et al. 2011

International Journal of Thermal Sciences

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“…For Ri > 1.0, the majority of the fluid interior is stagnant. Mansour et al (2004) worked on the numerical study of Soret effect on multiple steady state solutions induced by double diffusive convection in a square porous cavity. They considered the Darcy model and presented numerical results for Ra =100, Le = 0.1 and Soret number * Corresponding Author: satheesh.a@vit.ac.in; egsatheesh@gmail.com varying from -31.4 to 40.…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of Double-Diffusive Mixed Convective Flow in an Enclosed Square Cavity With Soret Effect

Satheesh¹,

Mohan²

2017

Frontiers in Heat and Mass Transfer

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In this study, a two-dimensional steady state double-diffusive mixed convective flow in a square cavity with Soret effect is presented. The numerical investigation is considered with two different conditions, (a) top and bottom walls move with same velocity (Uo) towards right and (b) top wall moves towards right and bottom wall moves towards left with the same velocity (Uo). The left and right walls remain stationary. The top and bottom walls are adiabatic; the left wall is maintained at high temperature and concentration. The right wall is maintained at low temperature and concentration. INTRODUCTIONThe combined effect of temperature and concentration gradients along with some externally applied forces in which heat and mass transfer occur simultaneously is known as double-diffusive mixed convection. Double-diffusive mixed convection in cavities is an area extensively investigated because of the multitude of engineering applications they are often encountered in. The aforementioned areas of research include nuclear reactors, solar collectors, cooling of electronic systems, chemical processing equipment, etc. Double-diffusive convection is also referred to as buoyancy driven flow induced by both temperature and concentration gradients. Bergman (1989) studied the influence of Soretinduced solutal buoyancy forces on the hydrodynamics and heat transfer rates of an initially uniform concentration fluid contained in an enclosure associated with natural convection. The effect of Soret phenomenon may or may not be important in natural convection. However, the Soret effect must be included in the analysis of the water-based binary fluid. Reima et al. (1993) carried out numerical studies for mixed convection in a driven cavity with a stable vertical temperature gradient. Flow is generated by the top horizontal boundary wall, which slides in its own plane at constant speed. A stabilizing externally-applied vertical temperature gradient is imposed on the system boundaries: the top wall is maintained at a higher temperature than the bottom wall. It was observed that at Ri < 1.0, in the bulk of the interior, fluids are well mixed, and temperature variations are small. For Ri > 1.0, the majority of the fluid interior is stagnant. . The findings were, that heat and mass transfer differs with the change in magnitude of the temperature and concentration gradients. These gradients decide the thermal and solutal dominant regions in the cavity. The effect of double-diffusive natural convection of water in a partially heated enclosure with Soret and Dufour effect around the density maximum is numerically analyzed by Nithyadevi et al. (2009). The temperature and concentration between the two walls are varied. They found that the rate of heat and mass transfer increases when the values of thermal Ra increase in all heating locations Frontiers in Heat and Mass TransferAvailable at www.ThermalFluidsCentral.org

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“…At this last point, the value of Rayleigh number is equal to the critical Rayleigh for the equivalent pure fluid. Recently, Mansour et al (2004) performed a numerical study of the Soret effect on multiple steady-state solutions induced by double diffusive convection in a square porous cavity. It was found that, depending on the value of the Soret parameter, one, two or three solutions are possible; namely, monocellular trigonometric flow, monocellular clockwise flow and bicellular flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical study of thermosolutal convection with Soret effect in a square cavity

Rebaï¹,

Mojtabi²,

Safi³

et al. 2008

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose-The purpose of this paper is to present a numerical and an analytical study of the thermohaline convection with Soret effect in a square enclosure filled with a binary fluid mixture. Design/methodology/approach-The horizontal boundaries of the enclosure are impermeable and heated from below while its vertical walls are assumed to be adiabatic and impermeable. The Navier-Stokes equations under the Boussinesq-Oberbeck approximation are solved numerically. The results are given for different values of the separation ratio. The critical Rayleigh number at the onset of convection is determined analytically and numerically. The Hopf frequency at the onset of convection is obtained. Findings-The existence of two stable stationary bifurcation branches is illustrated. Furthermore, it is shown that the existence of stable traveling waves in the transition from one branch to the other depends on the value of the separation ratio. For some values of Rayleigh number, asymmetric flows are observed. A good agreement is found between the numerical solution and analytical analysis. Originality/value-The present work is the first to consider thermosolutal convection with Soret effect in a square enclosure.

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Soret effect on double-diffusive multiple solutions in a square porous cavity subject to cross gradients of temperature and concentration

Cited by 18 publications

References 0 publications

Two- and three-dimensional multiple steady states in a porous cavity heated and salted from below

Two- and three-dimensional multiple steady states in a porous cavity heated and salted from below

Computational Investigation of Double-Diffusive Mixed Convective Flow in an Enclosed Square Cavity With Soret Effect

Numerical study of thermosolutal convection with Soret effect in a square cavity

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