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Research Papers

Analysis of Heat Transfer in Consecutive Variable Cross-Sectional Domains: Applications in Biological Media and Thermal Management

[+] Author and Article Information
Shadi Mahjoob

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

Kambiz Vafai1

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

1

Corresponding author.

J. Heat Transfer 133(1), 011006 (Sep 27, 2010) (9 pages) doi:10.1115/1.4002303 History: Received May 29, 2010; Revised July 31, 2010; Published September 27, 2010; Online September 27, 2010

Temperature prescription and control is important within biological media and in bioheat transport applications such as in hyperthermia cancer treatment in which the unhealthy tissue/organ is subject to an imposed heat flux. Thermal transport investigation and optimization is also important in designing heat management devices and small-scale porous-filled-channels utilized in electronic and biomedical applications. In this work, biological media or the stated heat management devices with a nonuniform geometry are modeled analytically as a combination of convergent, uniform and/or divergent configurations. The biological media is represented as blood saturated porous tissue matrix while incorporating cells and interstices. Two primary models, namely, adiabatic and constant temperature boundary conditions, are employed and the local thermal nonequilibrium and an imposed heat flux are fully accounted for in the presented analytical expressions. Fluid and solid temperature distributions and Nusselt number correlations are derived analytically for variable cross-sectional domain represented by convergent, divergent, and uniform or any combination thereof of these geometries while also incorporating internal heat generation in fluid and/or solid. Our results indicate that the geometrical variations have a substantial impact on the temperature field within the domain and on the surface with an imposed heat flux. It is illustrated that, the temperature distribution within a region of interest can be controlled by a proper design of the multisectional domain as well as proper selection of the porous matrix. These comprehensive analytical solutions are presented for the first time, to the best of the authors' knowledge in literature.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Schematic diagram of a channel filled with a porous medium subject to a constant heat flux on one side and either an adiabatic or a constant temperature wall on the other side (at the upper wall): (a) convergent channel, (b) uniform channel, (c) divergent channel, (d) variable cross-sectional domain made of convergent-uniform-divergent sections, and (e) variable cross-sectional domain made of divergent-uniform-convergent sections

Grahic Jump Location
Figure 2

Comparison of the present analytical fluid and solid temperature distributions at zero inclination angle with the analytical results of Lee and Vafai (29) and analytical-numerical results of Marafie and Vafai (30) for κ=100, q̇f=q̇s=0: (a) Bi=0.5 and (b) Bi=10

Grahic Jump Location
Figure 3

Fluid and solid temperature distributions at different axial locations of a variable cross-sectional domain made of convergent (α=5 deg)-uniform-divergent (α=5 deg) sections, subject to an adiabatic boundary at the upper wall for κ=0.01, q̇f=q̇s=0: (a) Bi=0.5 and (b) Bi=10

Grahic Jump Location
Figure 4

Fluid and solid temperature distributions at different axial locations of a variable cross-sectional domain made of divergent (α=5 deg)-uniform-convergent (α=5 deg) sections, subject to an adiabatic boundary at the upper wall for κ=0.01, q̇f=q̇s=0: (a) Bi=0.5 and (b) Bi=10

Grahic Jump Location
Figure 5

Temperature distributions at different axial locations of a variable cross-sectional domain made of (a) convergent (α=5 deg)-uniform-divergent (α=5 deg) sections; (b) divergent (α=5 deg)-uniform-convergent (α=5 deg) sections, subject to a constant temperature at the upper wall, for κ=0.01 and q̇f=q̇s=0.

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