Research Papers: Porous Media

Heat Transfer of Coupled Fluid Flow Within a Channel With a Permeable Base

[+] Author and Article Information
Rosemarie Mohais1

School of Mathematics and Statistics, University of South Australia, Mawson Lakes Campus, 5095 South Australia, Australiarosemarie.mohais@unisa.edu.au, rmohais@gmail.com

Balswaroop Bhatt

Department of Mathematics and Computer Science, University of the West Indies, St. Augustine, Trinidad and Tobagobal.bhatt@sta.uwi.edu, balswaroopbhatt@hotmail.com


Corresponding author.

J. Heat Transfer 131(11), 112601 (Aug 19, 2009) (8 pages) doi:10.1115/1.3154626 History: Received November 02, 2008; Revised April 23, 2009; Published August 19, 2009

We examine the heat transfer in a Newtonian fluid confined within a channel with a lower permeable wall. The upper wall of the channel is impermeable and driven by an accelerating surface velocity. Through a similarity solution, the Navier–Stokes equations are reduced to a fourth-order differential equation; the analytical solutions of which determined for small Reynolds numbers show dependence of the temperature and heat transfer profiles on the slip parameter based on the properties of the porous channel base. For larger Reynolds numbers, numerical solutions for three main groups of solutions show that the Reynolds number strongly influences the heat transfer profile. However, the slip conditions associated with the porous base of the channel can be used to alter these heat transfer profiles for large Reynolds numbers. The presence of a porous base in a channel can thus serve as an effective means of reducing or enhancing heat transfer performance in model systems.

Copyright © 2009 by American Society of Mechanical Engineers
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Figure 1

Channel with a fixed lower porous wall with an upper wall driven by a surface velocity

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Figure 2

Plot of ζ versus ϕ(ζ) and ϕ′(ζ)

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Figure 3

Longitudinal velocity profiles at Re=40, 90, 933.2, and 6574

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Figure 4

The temperature profile for Re=40

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Figure 5

The heat transfer profile for Re=40

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Figure 6

The heat transfer profile for Re=90

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Figure 7

The heat transfer profile for Re=381.7

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Figure 8

The heat transfer profile for Re=6574

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Figure 9

The heat transfer profile for Re=40 with 1/ax=1

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Figure 10

Variation in the Nusselt number for small Reynolds number for λ=10

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Figure 11

The heat transfer profile for Re=6574 for values of λ=0.001, 3, and 10

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Figure 12

Existence of thermal boundary layer close to lower permeable wall for high Reynolds number flow

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Figure 13

Variation in g′(y) with permeability for small Reynolds number for water

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Figure 14

Variation in g′(y) with permeability for small Reynolds number for air

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Figure 15

Variation in g′(y) with permeability for small Reynolds number for an arbitrary fluid of Pr=100



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