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Journal of Porous Media

Impact factor: 1.035

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v12.i4.10
pages 289-300

A Macroscopic Model for Countercurrent Bioheat Transfer in a Circulatory System

Akira Nakayama
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Naka-ku, Hamamatsu, 432-8561, Japan; Wuhan Polytechnic University, Wuhan, Hubei 430023, China
Fujio Kuwahara
Department of Mechanical Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561 Japan
Wei Liu
Huazhong University of Science and Technology (HUST), 1037 Luoyu Rd., Hongshan District, Wuhan 430074, China


The volume averaging theory of porous media has been applied to obtain a general set of macroscopic governing equations for countercurrent bioheat transfer between terminal arteries and veins in the circulatory system. Capillaries providing a continuous connection between the countercurrent terminal arteries and veins are modeled, introducing the perfusion bleed-off rate. Three distinctive energy equations are derived for the arterial blood phase, venous blood phase, and tissue phase. It has been found that the resulting model, under appropriate conditions, naturally reduces to those introduced by Chato, Bejan, Weinbaum and Jiji, and others for countercurrent heat transfer for the case of closely aligned pairs of vessels. A useful expression for the longitudinal effective thermal conductivity for the tissue has been derived without dropping the perfusion source terms. The expression turns out to be quite similar to Bejan's and Weinbaum and Jiji's expressions. Furthermore, the effect of spatial distribution of perfusion bleed-off rate on total countercurrent heat transfer has been investigated in depth exploiting the present bioheat transfer model.