A Model for Heat Transfer From Embedded Blood Vessels in Two-Dimensional Tissue Preparations

[+] Author and Article Information
Liang Zhu, Sheldon Weinbaum

Department of Mechanical Engineering, The City College of the City University of New York, New York, NY 10031

J Biomech Eng 117(1), 64-73 (Feb 01, 1995) (10 pages) doi:10.1115/1.2792272 History: Received March 29, 1993; Revised October 28, 1993; Online October 30, 2007


Two-dimensional microvascular tissue preparations have been extensively used to study blood flow in the microcirculation, and, most recently, the mechanism of thermal equilibration between thermally significant countercurrent artery-vein pairs. In this paper, an approximate three-dimensional solution for the heat transfer from a periodic array of blood vessels in a tissue preparation of uniform thickness with surface convection is constructed using a newly derived fundamental solution for a Green’s function for this flow geometry. This approximate solution is exact when the ratio K′ of the blood to tissue conductivity is unity and a highly accurate approximation when K′ ≠ 1. This basic solution is applied to develop a model for the heat transfer from a countercurrent artery-vein pair in an exteriorized rat cremaster muscle preparation. The numerical results provide important new insight into the design of microvascular experiments in which the axial variation of the thermal equilibration in microvessels can be measured for the first time. The solutions also provide new insight into the design of fluted fins and microchips that are convectively cooled by internal pores.

Copyright © 1995 by The American Society of Mechanical Engineers
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