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TECHNICAL PAPERS

Heat Transfer in a Laminar Channel Flow Generated by Injection Through Porous Walls

[+] Author and Article Information
Clarisse Fournier

Centre de Thermique de Lyon, UMR CNRS 5008, INSA de Lyon, Bat Sadi Carnot, 20 av. Albert Einstein, 69621 Villeurbanne Cedex, France

Marc Michard

Centre de Thermique de Lyon, UMR CNRS 5008, INSA de Lyon, Bat Sadi Carnot, 20 av. Albert Einstein, 69621 Villeurbanne Cedex, Franceclarisse.fournier@insa-lyon.fr

Françoise Bataille

 PROMES, UPR CNRS 8521, Rambla de la thermodynamique, Tecnosud, 66100 Perpignan, France

J. Fluids Eng 129(8), 1048-1057 (Mar 18, 2007) (10 pages) doi:10.1115/1.2746908 History: Received March 17, 2006; Revised March 18, 2007

Steady state similarity solutions are computed to determine the temperature profiles in a laminar channel flow driven by uniform fluid injection at one or two porous walls. The temperature boundary conditions are non-symmetric. The numerical solution of the governing equations permit to analyze the influence of the governing parameters, the Reynolds and Péclet numbers. For both geometries, we deduce a scaling law for the boundary layer thickness as a function of the Péclet number. We also compare the numerical solutions with asymptotic expansions in the limit of large Péclet numbers. Finally, for non-symmetric injection, we derive from the computed temperature profile a relationship between the Nusselt and Péclet numbers.

Copyright © 2007 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flow geometry (a) case a and (b) case b

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Figure 2

Sketch of the control volume

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Figure 3

Non-dimensional streamwise velocity profiles (a) case a and (b) case b

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Figure 4

Non-dimensional normal velocity profiles (a) case a and (b) case b

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Figure 5

Streamlines: – –: Rein=1 and —: Rein=1000(a) case a and (b) case b

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Figure 6

Evolution of K with the Reynolds number (a) case a and (b) case b

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Figure 7

Non-dimensional temperature profiles (a) case a and (b) case b

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Figure 8

Non-dimensional temperature profiles: Rein=10 and Rein=1000

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Figure 9

Scaling laws for f′(0) and f″(1)

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Figure 10

Scaling laws for the thermal boundary layer thickness (Eqs. 32,33)

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Figure 11

Computed, asymptotic, and modeled temperature profiles, Pr=1(a) case a and (b) case b

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Figure 12

Computed, asymptotic, and modeled temperature profiles, Pr=7(a) case a and (b) case b

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Figure 13

Evolution of the wall temperature with the Reynolds number (case b)

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Figure 14

Nusselt number as a function of Reynolds number

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Figure 15

Evolution of the number of mesh points with the tolerance ϵ=10−m (Rein=1000 and Pein=1)

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Figure 16

Location of the mesh points for Rein=50 and 100 and Pr=1(ϵ=10−12)

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Figure 17

Evolution of the computed functions with the tolerance ϵ=10−m (Rein=1000 and Pein=1)

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