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TECHNICAL PAPERS

# Natural Convection of a Two-Component Fluid in Porous Media Bounded by Tall Concentric Vertical Cylinders

[+] Author and Article Information
A. Bahloul, M. A. Yahiaoui, P. Vasseur

École Polytechnique, C. P. 6079, Succ. “Centre Ville” Montréal, Montreal, QC H3C 3A7, Canada

R. Bennacer, H. Beji

LEEVAM, Rue d’Eragny, Neuville sur Oise, Cergy-Pontoise Cedex, France

J. Appl. Mech 73(1), 26-33 (May 12, 2005) (8 pages) doi:10.1115/1.1993666 History: Received September 30, 2004; Revised May 12, 2005

## Abstract

This paper reports an analytical and numerical study of the behavior of a binary mixture saturating a vertical annular porous medium. Uniform heat fluxes are applied to the vertical walls while the horizontal walls are impermeable and adiabatic. Solutal gradients are assumed to be induced either by the imposition of constant gradients of concentration on the vertical walls (double diffusive convection, $a=0$) or by the Soret effect ($a=1$). Governing parameters of the problem under study are the thermal Rayleigh $RT$, buoyancy ratio $φ$, Lewis number $Le$, aspect ratio $A$, constant $a$, and curvature $η$. An analytical solution, valid for tall enclosures ($A⪢1$), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations. For large Rayleigh numbers ($RT⪢1$), an approximate solution valid in the limit of the boundary layer regime is obtained.

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Copyright © 2006 by American Society of Mechanical Engineers
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## Figures

Figure 1

Schematic diagram of the physical model and coordinate system

Figure 2

Contour lines of stream function (left), temperature (center), and concentration (right) for RT=50, φ=−0.8, Le=10, a=1, and A=1 ; (a) η=1 ; (b) η=0.1

Figure 3

Contour lines of stream function (left), temperature (center), and concentration (right) for RT=50, φ=−0.8, Le=10, a=1, η=0.1, and A=10

Figure 4

Comparison between analytical and numerical solutions for the case φ=1, Le=10, and η=0.3. Effect of RT on Ω,Ψ0, Nu and Sh for a=0 (double diffusive convection)

Figure 5

Comparison between analytical and boundary layer solutions for the case φ=0.01, Le=10, a=1 and various values of η; effect of RT on Nu and Sh

Figure 6

Contour lines of stream function (left), temperature (center), and concentration (right) for RT=50, Le=10, η=0.5, a=1, and A=8; (a) φ=0, (b) φ=10, and (c) φ=−10

Figure 7

Effect of the buoyancy ratio φ on the amplitude Ψ0 for the case RT=50, Le=10, a=1, and various values of η

Figure 8

Contour lines of stream function (left), temperature (center), and concentration (right) for RT=50, Le=10, φ=−1.8, a=1, A=4, and (a) η=1 and (b) η=0.5

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