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# The Effect of a Transition Layer Between a Fluid and a Porous Medium: Forced Convection in a Channel

[+] Author and Article Information
A. V. Kuznetsov

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

D. A. Nield

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

J. Heat Transfer 130(9), 094504 (Jul 14, 2008) (5 pages) doi:10.1115/1.2945905 History: Received November 19, 2007; Revised February 11, 2008; Published July 14, 2008

## Abstract

Flow in a three-layer channel is modeled analytically. The channel consists of a transition layer sandwiched between a porous medium and a fluid clear of solid material. Within the transition layer, the reciprocal of the permeability varies linearly across the channel. The Brinkman model is used for the momentum equations for the porous medium layer and the transition layer. The velocity profile is obtained in closed form in terms of Airy, exponential, and polynomial functions and this is employed to find analytically the Nusselt number for fully developed forced convection with boundaries subject to uniform and constant heat flux.

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## Figures

Figure 2

Plots of the Nusselt number as a function of conductivity ratios for various values of the Darcy number (a) Da=1, (b) Da=0.01, and (c) Da=0.0002, for a thin transition layer (ξ=0.49, η=0.51)

Figure 1

Plots of the Nusselt number as a function of conductivity ratios for various values of the Darcy number (a) Da=1, (b) Da=0.01, and (c) Da=0.0002, for a fat transition layer (ξ=1∕3, η=2∕3)

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