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RESEARCH PAPER

An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and Uniform Dirichlet Boundary Conditions

[+] Author and Article Information
Devashish Shrivastava

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84102

Benjamin McKay

Department of Mathematics, University of Utah, Salt Lake City, UT 84102

Robert B. Roemer

Department of Mechanical Engineering, University of Utah, Salt Lake City, UT 84102e-mail: bob.roemer@utah.edu

J. Heat Transfer 127(2), 179-188 (Mar 15, 2005) (10 pages) doi:10.1115/1.1842788 History: Received January 23, 2004; Revised September 01, 2004; Online March 15, 2005
Copyright © 2005 by ASME
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Figures

Grahic Jump Location
Schematic of the tissue cylinder with two unequal arbitrarily located vessels
Grahic Jump Location
Dividing the original problem of two vessels in a finite tissue into two sub-problems, each consisting of one vessel only
Grahic Jump Location
The validity of the solution is presented for N=20,P=20,Rvw1=0.2,Av1=−0.6,Rvw2=0.4, and Av2=0.4. Solid lines represent the given nondimensional temperatures at the two vessel walls and the outer tissue boundary. The solution predicted using the solution is presented using markers.
Grahic Jump Location
The variation in the nondimensional vessel–vessel heat transfer rate, Qvw,2-vw,1, as a function of the nondimensional vessel 2 size, Rvw2, and eccentricity, Av2, with Rvw1=0.2,Av1=−0.6,Tvw1=0,Tvw2=0.6,Ttw=1, and P=0, 10, 20
Grahic Jump Location
The variation in the nondimensional heat transfer rate from tissue to vessel 1, Qtw-vw1, as a function of the nondimensional vessel 2 size, Rvw2, and eccentricity, Av2, with Rvw1=0.2,Av1=−0.6,Tvw1=0,Tvw2=0.6,Ttw=1
Grahic Jump Location
The variation in the nondimensional heat transfer rate from tissue to vessel 2, Qtw-vw2, as a function of the nondimensional vessel 2 size, Rvw2, and eccentricity, Av2, with Rvw1=0.2,Av1=−0.6,Tvw1=0,Tvw2=0.6,Ttw=1
Grahic Jump Location
The variation in the vessel–vessel heat transfer rate, qvw2-vw1, as a fraction of the tissue to vessel 1 heat transfer rate, qtw-vw1, as a function of the nondimensional vessel 2 size, Rvw2, and eccentricity, Av2, with Rvw1=0.2,Av1=−0.6,Tvw1=0,Tvw2=0.6,Ttw=1
Grahic Jump Location
The variation in the vessel–vessel heat transfer rate, qvw2-vw1, as a fraction of the tissue to vessel 2 heat transfer rate, qtw-vw2, as a function of the nondimensional vessel 2 size, Rvw2, and eccentricity, Av2, with Rvw1=0.2,Av1=−0.6,Tvw1=0,Tvw2=0.6,Ttw=1

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