Conditions for Equivalency of Countercurrent Vessel Heat Transfer Formulations

[+] Author and Article Information
R. B. Roemer

Department of Mechanical Engineering, and Department of Radiation Oncology, The University of Utah, Salt Lake City, UT 84112

J Biomech Eng 121(5), 514-520 (Oct 01, 1999) (7 pages) doi:10.1115/1.2835081 History: Received March 10, 1998; Revised April 22, 1999; Online January 23, 2008


Previous models of countercurrent blood vessel heat transfer have used one of two, different, equally valid but previously unreconciled formulations, based either on: (1) the difference between the arterial and venous vessels’ average wall temperatures, or (2) the difference between those vessels’ blood bulk fluid temperatures. This paper shows that these two formulations are only equivalent when the four, previously undefined, “convective heat transfer coefficients” that are used in the bulk temperature difference formulation (two coefficients each for the artery and vein) have very specific, problem-dependent relationships to the standard convective heat transfer coefficients. (The average wall temperature formulation uses those standard coefficients correctly.) The correct values of these bulk temperature difference formulation “convective heat transfer coefficients” are shown to be either: (1) specific functions of (a) the tissue conduction resistances, (b) the standard convective heat transfer coefficients, and (c) the independently specified bulk arterial, bulk venous and tissue temperatures, or (2) arbitrary, user defined values. Thus, they are generally not equivalent to the standard convective heat transfer coefficients that are regularly used, and must change values depending on the blood and tissue temperatures. This dependence can significantly limit the convenience and usefulness of the bulk temperature difference formulations.

Copyright © 1999 by The American Society of Mechanical Engineers
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