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Research Papers: Porous Media

Forced Convection in a Channel Partly Occupied by a Bidisperse Porous Medium: Symmetric Case

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

Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealandd.nield@auckland.ac.nz

A. V. Kuznetsov

Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910avkuznet@eos.ncsu.edu

J. Heat Transfer 133(7), 072601 (Apr 05, 2011) (9 pages) doi:10.1115/1.4003667 History: Received March 26, 2010; Revised February 14, 2011; Published April 05, 2011; Online April 05, 2011

An analytic solution is obtained for the problem of fully developed forced convection in a channel between parallel plane walls, partly occupied by a bidisperse porous medium (BDPM) and partly by a fluid clear of solid material, the distribution of material being symmetrical with the BDPM forming either the core or the sheath portion of the channel. The case of uniform flux boundaries is considered. For the porous medium, a two-velocity two-temperature model based on Darcy’s law is employed and the Beavers–Joseph interface condition is imposed. In each case, Nusselt number values are obtained in terms of various parameters.

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Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Schematic definition sketch. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 2

Plot of the Nusselt number Nu versus the interphase velocity ratio Ur for various values of the conductivity ratio kr and the interphase heat transfer parameter γ. ξ=0.5, ϕ=0.5, and N=1. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 3

Plot of the Nusselt number Nu versus the conductivity ratio kr for various values of the interphase velocity ratio Ur and the interphase heat transfer parameter γ. ξ=0.5, ϕ=0.5, and N=1. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 4

Plot of the Nusselt number Nu versus the interphase heat transfer parameter γ for various values of the interphase velocity ratio Ur and the conductivity ratio kr. ξ=0.5, ϕ=0.5, and N=1. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 5

Plot of the Nusselt number Nu versus the hydrodynamic interface parameter N for various values of the interphase velocity ratio Ur and the conductivity ratio kr. ξ=0.5, ϕ=0.5, and γ=10. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 6

Plot of the Nusselt number Nu versus the interface position coordinate ξ for various values the of hydrodynamic interface parameter N. ϕ=0.5, Uf=1, Ur=1, kr=1, and γ=100. (a) BDPM core and (b) BDPM sheath.

Grahic Jump Location
Figure 7

Magnified plots of portions of the plots in Fig. 6

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