Double diffusive convection in a vertical enclosure filled with anisotropic porous media

Bennacer, Rachid; Tobbal, A.; Béji, H.; Vasseur, P.

doi:10.1016/s1290-0729(00)01185-6

Cited by 77 publications

(28 citation statements)

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“…In Beji et al (1999) for Ra T = 500, Le = 10, N = 0, and λ = 5 theory, the case of infinite curvature characterized by λ = 1 represents a rectangular cavity. The comparison shown in Table 3 reveals that the detected maximum difference with the results of Goyeau et al (1996) and Bennacer et al (2001) is less than 2.3%. From Fig.…”

Section: Validationmentioning

confidence: 90%

“…Figure 2 exhibits the good agreement between the present streamlines, isotherms and isoconcentrations and that of Beji et al (1999) in a uniformly heated and salted porous annulus. In addition to the above validation, we also compare our results with Goyeau et al (1996) and Bennacer et al (2001) in a rectangular porous cavity (λ=1). In Beji et al (1999) for Ra T = 500, Le = 10, N = 0, and λ = 5 theory, the case of infinite curvature characterized by λ = 1 represents a rectangular cavity.…”

Section: Validationmentioning

confidence: 92%

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Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

et al. 2011

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This article reports a numerical study of double-diffusive convection in a fluidsaturated vertical porous annulus subjected to discrete heat and mass fluxes from a portion of the inner wall. The outer wall is maintained at uniform temperature and concentration, while the top and bottom walls are adiabatic and impermeable to mass transfer. The physical model for the momentum equation is formulated using the Darcy law, and the resulting governing equations are solved using an implicit finite difference technique. The influence of physical and geometrical parameters on the streamlines, isotherms, isoconcentrations, average Nusselt and Sherwood numbers has been numerically investigated in detail. The location of heat and solute source has a profound influence on the flow pattern, heat and mass transfer rates in the porous annulus. For the segment located at the bottom portion of inner wall, the flow rate is found to be higher, whereas the heat and mass transfer rates are higher when the source is placed near the middle of the inner wall. Further, the average Sherwood number increases with Lewis number, while for the average Nusselt number the effect is opposite. The average Nusselt number increases with radius ratio (λ); however, the average Sherwood number increases with radius ratio only up to λ = 5, and for λ > 5 , the average Sherwood number does not increase significantly.123 754 M. Sankar et al.

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Section: Validationmentioning

confidence: 90%

Section: Validationmentioning

confidence: 92%

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

et al. 2011

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“…To further validate the present numerical code, the double diffusive natural convection in square uniform porous enclosure, where the two vertical walls are maintained at uniform and different temperatures and concentrations, has been numerically analyzed for R t = 10 2 −−2.0 × 10 3 , Le = 10, 100, and N = 0 (heat-transfer- Goyeau et al (1996), Bennacer et al (2001), and Bourich et al (2004) for the case of isotropic porous media on heat-transfer-driven flows (N = 0, AR = 1, B = 1) driven flows). In general, the results presented in Table 1 are in good agreement with those of Goyeau et al (1996), Bennacer et al (2001), and Bourich et al (2004). The accuracy of the numerical code is also checked with the steady results reported by Mamou et al (1995) in the case of double diffusive convection within a square porous enclosure subject to horizontal and uniform heat and mass fluxes.…”

Section: Numerical Technique and Code Validationmentioning

confidence: 99%

“…A comprehensive review of the literature concerning double-diffusive natural convection in a fluid-saturated porous medium may be found in the books by Ingham and and Nield and Bejan (2006). In these studies, uniform boundary conditions imposed along the vertical boundaries have been studied, including constant temperature and concentration boundaries (Goyeau et al 1996;Beji et al 1999;Bennacer et al 2001;Chamkha and Al-Naser 2001;Chamkha 2002;Costa 2004); Uniform heat and mass fluxes boundary conditions (Mamou et al, 1995); Mixing Dirichlet and Neumann boundary conditions (Mamou 2002). Besides, the linear distributions of temperature and concentration along the vertical side have been considered by Kumar et al (2002) and Kumar and Shalini (2005).…”

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confidence: 99%

Free convection from one thermal and solute source in a confined porous medium

2007

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This paper reports a numerical study of double diffusive natural convection in a vertical porous enclosure with localized heating and salting from one side. The physical model for the momentum conservation equation makes use of the Darcy equation, and the set of coupled equations is solved using the finite-volume methodology together with the deferred central difference scheme. An extensive series of numerical simulations is conducted in the range of −10 N +10, 0 R t 200, 10 −2 Le 200, and 0.125 L 0.875, where N, R t , Le, and L are the buoyancy ratio, Darcy-modified thermal Rayleigh number, Lewis number, and the segment location. Streamlines, heatlines, masslines, isotherms, and iso-concentrations are produced for several segment locations to illustrate the flow structure transition from solutal-dominated opposing to thermal dominated and solutal-dominated aiding flows, respectively. The segment location combining with thermal Rayleigh number and Lewis number is found to influence the buoyancy ratio at which flow transition and flow reversal occurs. The computed average Nusselt and Sherwood numbers provide guidance for locating the heating and salting segment.

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“…The Brinkman's extension of Darcy's law has been used in a study by Bennacer et al (2001) to investigate double-diffusive convection in anisotropic porous media with high porosity. It is demonstrated that the anisotropic properties of the porous medium considerably modify the heat and mass transfer rates from that expected under isotropic conditions.…”

Section: Introductionmentioning

confidence: 99%

Density Maximum Effect on Double-diffusive Natural Convection in a Porous Cavity with Variable Wall Temperature

2007

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The effect of density maximum of water on double-diffusive natural convection in a two-dimensioned cavity filled with a water saturated isotropic porous medium is studied numerically. The horizontal walls of the cavity are insulated. The opposing vertical walls are kept at different temperatures θ h (linearly varies with height) and θ c (θ c ≤ θ h ). The concentration levels at cold wall and hot wall are, respectively, c 1 and c 2 with c 1 > c 2 . Brinkman-Forchheimer extended Darcy model is used to investigate the average heat and mass transfer rates. The non-dimensional equations for momentum, energy, and concentration are solved by finite volume method with power law scheme for convection and diffusion terms. The results are presented in the form of streamlines, isotherms, and isoconcentration lines for various values of Grashof numbers, Schmidt number, porosity, and Darcy numbers. It is observed that the density maximum of water has profound effect on the thermosolutal convection. The effects of different parameters on the velocity, temperature, and species concentrations are also shown graphically.

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Double diffusive convection in a vertical enclosure filled with anisotropic porous media

Cited by 77 publications

References 0 publications

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

Double-Diffusive Convection from a Discrete Heat and Solute Source in a Vertical Porous Annulus

Free convection from one thermal and solute source in a confined porous medium

Density Maximum Effect on Double-diffusive Natural Convection in a Porous Cavity with Variable Wall Temperature

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