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Research Papers: Bio-Heat and Mass Transfer

Analysis of Bioheat Transport Through a Dual Layer Biological Media

[+] 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 132(3), 031101 (Dec 30, 2009) (14 pages) doi:10.1115/1.4000060 History: Received June 10, 2009; Revised August 12, 2009; Published December 30, 2009; Online December 30, 2009

A comprehensive analysis of bioheat transport through a double layer and multilayer biological media is presented in this work. Analytical solutions have been developed for blood and tissue phase temperatures and overall heat exchange correlations, incorporating thermal conduction in tissue and vascular system, blood-tissue convective heat exchange, metabolic heat generation, and imposed heat flux, utilizing both local thermal nonequilibrium and equilibrium models in porous media theory. Detailed solutions as well as Nusselt number distributions are given, for the first time, for two primary conditions, namely, isolated core region and uniform core temperature. The solutions incorporate the pertinent effective parameters for each layer, such as volume fraction of the vascular space, ratio of the blood, and the tissue matrix thermal conductivities, interfacial blood-tissue heat exchange, tissue/organ depth, arterial flow rate and temperature, body core temperature, imposed hyperthermia heat flux, metabolic heat generation, and blood physical properties. Interface temperature profiles are also obtained based on the continuity of temperature and heat flux through the interface and the physics of the problem. Comparisons between these analytical solutions and limiting cases from previous works display an excellent agreement. These analytical solutions establish a comprehensive presentation of bioheat transport, which can be used to clarify various physical phenomena as well as establishing a detailed benchmark for future works in this area.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic diagram of (a) the multilayer tissue-vascular system, (b) model I (peripheral heat flux or isolated core region), and (c) model II (uniform core temperature)

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Figure 2

Comparison of the temperature profiles obtained from double layer analytical solution with similar properties (utilizing two equation modeling) with those obtained from a single layer model (7) for blood and tissue phases with model I (isolated core region) for κ=0.111, ξb=0.111, ξt=1, ε1=ε2=0.1 and Bi1=Bi2=10, (a) D=1, (b) D=2, and (c) D=1/2

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Figure 3

Comparison of the temperature profiles obtained from double layer analytical solution with similar properties (utilizing one equation modeling) with those obtained from a single layer model (7), for model I (isolated core region) with κ=0.111, ξb=0.111, ξt=1, ε1=ε2=0.1 and Bi1=Bi2=10, (a) D=1, (b) D=2, and (c) D=1/2

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Figure 4

Comparison of the temperature profiles obtained from the first layer of the double layer analytical solution with those obtained from a single layer model (7) for model II (uniform core temperature) with κ=0.111, ξb=0.111, ξt=1, ε1=ε2=0.1, and Bi1=Bi2=10, utilizing (a) two equation and (b) one equation models

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Figure 5

The effect of vascular volume fraction variation in biological layers, for model I (isolated core region), for similar blood and tissue properties in the layers, D=1, Bi1=Bi2=10, Φ1/(1−ε1)=Φ2/(1−ε2)=0.55, (a) tissue phase, (b) blood phase

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Figure 6

The effect of metabolic heat generation in biological layers, for model I (isolated core region), for similar blood and tissue properties in the layers, D=1, κ=0.111, ξb=0.111, ξt=1, ε1=ε2=0.1, Bi1=Bi2=10, (a) tissue phase, (b) blood phase

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