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TECHNICAL PAPERS: Porous Media

Heat Transfer Associated to Natural Convection Flow in a Partly Porous Cavity

[+] Author and Article Information
Jean-François Mercier, Catherine Weisman, Mouaouia Firdaouss, Patrick Le Quéré

LIMSI-CNRS, BP 133, F-91403 Orsay Cedex, France

J. Heat Transfer 124(1), 130-143 (Jun 25, 2001) (14 pages) doi:10.1115/1.1418372 History: Received September 26, 2000; Revised June 25, 2001
Copyright © 2002 by ASME
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Figures

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Problem geometry (a) and steady flow in a cavity of aspect ratio 4, with heat flux imposed on the sides. A porous layer covers the heated wall and fills one quarter of the cavity. Ra=106,Da=10−4: (b) streamlines, (c) isothermal lines.
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Problem geometry and vertical flow w0(x) in the central part of the cavity
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Comparison of dimensionless vertical velocity profiles (left) and temperature profiles (right) at mid-height of the cavity for r=1 and r=10 for one given numerical setup, A=4,Ra=106,Da=10−4,ep=0.25
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Steady state profiles w0(x) and θ0(x) for Ra=106,ep=0.5, and γ varying in the range [15,35]: (a) Da=1, (b) Da=10−4, and (c) Da=10−6
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Steady-state profiles w0(x) and θ0(x) for Ra=106,ep=0.5, and γ varying in the range [2,15]: (a) Da=1, (b) Da=10−3, and (c) Da=10−6
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Velocity profiles w0(x) for Ra=106,Da=10−6,γ=15 and three values of ep: ep=0.25,ep=0.5, and ep=0.75
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Velocity profiles w0(x) for Ra=106,Da=10−6,ep=0.25 and three values of γ: γ=5,γ=10 and γ=20
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Location of the control volume, with boundary S shown in bold line
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Vertical temperature profile obtained from two-dimensional numerical simulations at mid-width of the cavity for Da=10−4,ep=0.25,Ra=106,A=5. A least squared approximation for the central linear region is shown.
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Vertical temperature profile obtained from two-dimensional numerical simulations at mid-width of the cavity for several aspect ratios: (a) fluid cavity, Ra=106; (b) Da=10−4,ep=0.25,Ra=106.
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Vertical temperature gradient γ versus the Darcy number Da for different heating strengths Ra, ep=0.5: (a) Ra∊[105,5.107]; and (b) Ra∊[104,5.104].
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log(γf) versus log(Ra), with 12 values of Ra shown
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(a) ln(γmax) versus ln(ep). Each line corresponds to a value of Ra, and on each line, each point corresponds to a value of ep. There are twelve Ra values in the [104,5.107] range, and eight ep values in the [0.25,0.8] range; (b) c(γf) versus the stratification parameter γf in the entirely fluid layer, each point corresponds to one of the 12 Ra values of (a); (c) a versus ln(Ra), each point corresponds to one of the 12 Ra values of (a); (d) b versus Ra, each point corresponds to one of the 12 Ra values of (a).
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(a) log(γmax) versus log(Ra). Each line corresponds to a value of ep, and on each line, each point corresponds to a value of Ra. There are twelve Ra values in the [104,5.107] range, and five ep values in the [0.5,0.8] range; (b) log(γmax) versus log(Da), same ep values and Ra values as in (a); (c) function d(ep) versus ep, all eight ep values in the [0.25,0.8] range; (d) ln(γmax/P2(ep)) versus ln(Ra/Damax), all ep values and Ra values.
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γmax (a) and Damax (b) calculated from the analytical fit versus the same quantities calculated directly from the model equations. All points shown (12 values of Ra and 8 values of ep).
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γmaxf calculated from the analytical fit (solid curves) and calculated directly from the model equations (points) versus (a) Ra and (b) Damax. All points shown (12 values of Ra and 8 values of ep, bottom ep=0.1 to top ep=0.8).
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Nusselt number Nu versus Da, top: ep=0.25, bottom: ep=0.75; (left) Ra∊[105,5.107] (right): Ra∊[104,5.104].
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Nusselt number versus Darcy number for various ep values, Ra=105

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