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Research Papers

Thermosolutal Natural Convection in Partially Porous Domains

[+] Author and Article Information
Dominique Gobin1

 Laboratoire FAST, CNRS, Université Pierre et Marie Curie, 91405 Orsay Cedex, Francegobin@fast.u-psud.fr

Benoît Goyeau

 Laboratoire EM2C, CNRS, École Centrale de Paris, 92295 Châtenay-Malabry Cedex, Francebenoit.goyeau@em2c.ecp.fr

1

Corresponding author.

J. Heat Transfer 134(3), 031013 (Jan 18, 2012) (10 pages) doi:10.1115/1.4005147 History: Received July 28, 2010; Revised June 24, 2011; Published January 18, 2012; Online January 18, 2012

In many industrial processes or natural phenomena, coupled heat and mass transfer and fluid flow take place in configurations combining a clear fluid and a porous medium. Since the pioneering work by Beavers and Joseph (1967), the modeling of such systems has been a controversial issue, essentially due to the description of the interface between the fluid and the porous domains. The validity of the so-called one-domain approach—more intuitive and numerically simpler to implement—compared to a two-domain description where the interface is explicitly accounted for, is now clearly assessed. This paper reports recent developments and the current state of the art on this topic, concerning the numerical simulation of such flows as well as the stability studies. The continuity of the conservation equations between a fluid and a porous medium are examined and the conditions for a correct handling of the discontinuity of the macroscopic properties are analyzed. A particular class of problems dealing with thermal and double diffusive natural convection mechanisms in partially porous enclosures is presented, and it is shown that this configuration exhibits specific features in terms of the heat and mass transfer characteristics, depending on the properties of the porous domain. Concerning the stability analysis in a horizontal layer where a fluid layer lies on top of a porous medium, it is shown that the onset of convection is strongly influenced by the presence of the porous medium. The case of double diffusive convection is presented in detail.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic description of the problem

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Figure 2

Mass transfer variation with permeability and porous layer thickness (RaT  = 106 , N = 10, Pr = 10, A = 2)

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Figure 3

Heat transfer variation with permeability and porous layer thickness (RaT  = 106 , N = 10, Pr = 10, A = 2, Le = 100)

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Figure 4

Flow structure around the first Nu number minimum: 5 × 10−8  < Da < 5 × 10−7 ; Δψ = 0.1 (RaT  = 106 , N = 10, xp  = 0.1, Le = 100, Pr = 10, A = 2). For comparing the flow structures, the streamlines have been plotted using the maximum value of the ψmax for all cases (ψ = 0 at the walls and Δψ = 0.1)

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Figure 5

Heat transfer variation with permeability for different Lewis numbers (RaT  = 106 , N = 10, xP  = 0.1, Pr = 10, A = 2)

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Figure 6

Heat transfer variation with permeability for different buoyancy ratios (RaT  = 106 , xP  = 0.1, Pr = 10, Le = 100, A = 2)

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Figure 7

Geometric configuration of the problem

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Figure 8

Marginal stability curves: comparison between the 1Ω and the 2ΩDB approaches for d̂=df*/dm*=0.08 and d̂=0.10 (Da = 7.4410−6 )

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Figure 9

Influence of the stress jump coefficient β for d̂=0.10 Da = 10−5 , ɛ = 0.39

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Figure 10

Critical solutal Rayleigh number versus the thermal Rayleigh number, for three values of the depth ratio d̂

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Figure 11

Wave number versus the thermal Rayleigh number, for three values of the depth ratio d̂

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Figure 12

Streamline patterns and vertical velocity profiles for d̂=0.8: (a) RaT  = −20, RaS  = −35.1 and κcr  = 10.2; (b) RaT  = 0, RaS  = 0 and κcr  = 6.0; (c) RaT  = 20, RaS  = 24.7 and κcr  = 3.5; (d) RaT  = 50, RaS  = 38 and κcr  = 4.0. The thick horizontal line represents the fluid/porous interface

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Figure 13

Influence of the thermal diffusivity ratio ɛT for d̂=0.8 and different thermal Rayleigh numbers

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