This paper presents a three-dimensional analysis of the temperature field around a pair of countercurrent arteries and veins embedded in an infinite tissue that has an arbitrary temperature gradient along the axes of the vessels. Asymptotic methods are used to show that such vessels are thermally similar to a highly conductive fiber in the same tissue. Expressions are developed for the effective radius and thermal conductivity of the fiber so that it conducts heat at the same rate that the artery and vein together convect heat and so that its local temperature equals the mean temperature of the vessels. This result allows vascular tissue to be viewed as a composite of conductive materials with highly conductive fibers replacing the convective effects of the vasculature. By characterizing the size and thermal conductivity of these fibers, well-established methods from the study of composites may be applied to determine when an effective conductive model is appropriate for the tissue and vasculature as a whole.
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Heat Transport by Countercurrent Blood Vessels in the Presence of an Arbitrary Temperature Gradient
J. W. Baish
J. W. Baish
Department of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837
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J. W. Baish
Department of Mechanical Engineering, Bucknell University, Lewisburg, PA 17837
J Biomech Eng. May 1990, 112(2): 207-211 (5 pages)
Published Online: May 1, 1990
Article history
Received:
February 1, 1989
Revised:
February 1, 1990
Online:
March 17, 2008
Citation
Baish, J. W. (May 1, 1990). "Heat Transport by Countercurrent Blood Vessels in the Presence of an Arbitrary Temperature Gradient." ASME. J Biomech Eng. May 1990; 112(2): 207–211. https://doi.org/10.1115/1.2891173
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