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Research Papers: Porous Media

Analytical Characterization and Production of an Isothermal Surface for Biological and Electronic Applications

[+] Author and Article Information
Shadi Mahjoob

Mechanical Engineering Department, University of California, Riverside, CA 92521

Kambiz Vafai1

Mechanical Engineering Department, University of California, Riverside, CA 92521vafai@engr.ucr.edu

1

Corresponding author.

J. Heat Transfer 131(5), 052604 (Mar 19, 2009) (12 pages) doi:10.1115/1.2995690 History: Received March 12, 2008; Revised July 09, 2008; Published March 19, 2009

Characterization and regulation of isothermal surfaces are key issues in a number of thermal management devices. The surface temperature uniformity can be controlled utilizing a variable area channel heat exchanger filled with a porous medium. A comprehensive analytical investigation of forced convection through a generic variable area channel is carried out to design a compact heat exchanger in producing an isothermal surface subject to a constant heat flux, which may be required in the biological, electronics, optical, laser, manufacturing, and solidification applications. Exact solutions for the fluid and solid phases and the wall surface temperature distributions as well as the Nusselt number correlations are established while incorporating local thermal nonequilibrium and transverse conduction contributions. The channel temperature field is adjusted utilizing either an adiabatic or a constant temperature on the inclined surface. The effects of the pertinent physical parameters, such as channel inlet/outlet thickness, inclination angle, Biot number, ratio of fluid and matrix thermal conductivities, working fluid properties, and imposed heat flux, on the fluid and solid temperature fields and the isothermal surface are thoroughly investigated. The results indicate that utilizing proper pertinent parameters, an isothermal surface is achieved. The validity of the utilization of the local thermal equilibrium model is also investigated and error maps are presented.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of a channel filled with a porous medium subject to a constant heat flux; Case I: adiabatic boundary condition at the upper wall, Case II: constant surface temperature boundary condition at the upper wall

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Figure 2

Comparison of the present analytical temperature distributions for fluid and solid phases with analytical solutions by Lee and Vafai (28) and Marafie and Vafai (29) at α=0deg and Bi=10. (a) κ=100 and (b) κ=0.01.

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Figure 3

Comparison of the present analytical temperature distributions for fluid and solid phases with analytical solutions by Lee and Vafai (28) and Marafie and Vafai (29) at α=0deg and Bi=0.5. (a) κ=100 and (b) κ=0.01.

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Figure 4

Comparison of the temperature distribution for the one equation model obtained from the present analytical work, with the analytical solution of Lee and Vafai (28) and computational simulation for κ=5×10−5 and α=0deg

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Figure 5

Comparison of the present analytical temperature distributions (utilizing the exact solutions of two and one equation models) with the numerical simulations at α=2deg, Bi=100, and κ=5×10−5. (a) X=1 and (b) X=4.

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Figure 6

Comparison between the wall temperature profile obtained from the present analytical solution and numerical simulation utilizing one equation model, at the inclination angles of 0deg and 5deg

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Figure 7

Effect of inclination angle on fluid and solid temperature fields for Bi=10 at X=2. (a) κ=100 and (b) κ=0.01.

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Figure 8

Effect of inclination angle on fluid and solid temperature fields for Bi=0.5 at X=2. (a) κ=100 and (b) κ=0.01.

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Figure 9

Effect of the inclination angle (α), flow rate, and effective thermal conductivity ratio (κ) on the normalized wall temperature distribution for Bi=10

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Figure 10

Effect of the inclination angle (α) and effective thermal conductivity ratio (κ) on the normalized wall temperature distribution for Bi=0.5 and Re=Re1

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Figure 11

Effect of the upper wall temperature (Case II) on the isothermal surface production for Bi=10, κ=0.01, and α=0

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Figure 12

Error maps on the validity of local thermal equilibrium model in the variable area channel heat exchanger: (a) ψ=1, (b) ψ=0.75, (c) ψ=0.5, and (d) ψ=0.25

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