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Research Papers: Porous Media

Vertical Free Convective Boundary-Layer Flow in a Bidisperse Porous Medium

[+] Author and Article Information
D. A. Rees

Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK

D. A. Nield

Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealand

A. V. Kuznetsov

Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910

J. Heat Transfer 130(9), 092601 (Jul 11, 2008) (9 pages) doi:10.1115/1.2943304 History: Received June 14, 2007; Revised October 24, 2007; Published July 11, 2008

In this article, we study the effect of adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM), on the classical Cheng–Minkowycz study of vertical free convection boundary-layer flow in a porous medium. It is shown that the boundary-layer equations can be expressed in terms of three parameters: a modified volume fraction, a modified thermal conductivity ratio, and a third parameter incorporating both thermal and BDPM properties. A numerical simulation of the developing boundary layer is guided by a near-leading-edge analysis and supplemented by a far-field analysis. The study is completed by a presentation of numerical simulations of the elliptic equations in order to determine how the adoption of the BDPM model affects the thermal fields in the close vicinity of the origin.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Sketch of a BDPM adjacent to a vertical plate

Grahic Jump Location
Figure 2

Variation of Qf (continuous lines) and Qp (long dashes) with ξ for τ=0.5 and γ=1, where δ takes the values of 1deg, 10deg, 20deg, 30deg, 40deg, and 44.9deg. Also shown are the four-term small-ξ expansions (dotted lines).

Grahic Jump Location
Figure 3

Variation of Qf (continuous lines) and Qp (long dashes) with ξ for τ=0.5 and δ=30deg, where γ takes the values of 10−2, 10−1, 1, 10, 102, and 103. Also shown are the four-term small-ξ expansions (dotted lines).

Grahic Jump Location
Figure 4

Variation of Qf (continuous lines) and Qp (long dashes) with ξ for γ=10−2 and δ=30deg, where τ takes the values of 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6

Grahic Jump Location
Figure 5

Isotherms for both the fluid phase (continuous lines) and solid phase (dashed lines) for γ=1.0, τ=1, δ=0 for various values of H

Grahic Jump Location
Figure 6

Isotherms for both the fluid phase (continuous lines) and solid phase (dashed lines) for γ=1.0, τ=0.8, H=0.001 for various values of δ

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