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首页> 外文期刊>Journal of Heat Transfer >An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and Uniform Dirichlet Boundary Conditions
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An Analytical Study of Heat Transfer in Finite Tissue With Two Blood Vessels and Uniform Dirichlet Boundary Conditions

机译：具有两个血管和均匀Dirichlet边界条件的有限组织中的传热分析研究

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Counter-current (vessel-vessel) heat transfer has been postulated as one of the most important heat transfer mechanisms in living systems. Surprisingly, however, the accurate quantification of the vessel-vessel, and vessel-tissue, heat transfer rates has never been performed in the most general and important case of a finite, unheated/heated tissue domain with noninsulated boundary conditions. To quantify these heat transfer rates, an exact analytical expression for the temperature field is derived by solving the 2-D Poisson equation with uniform Dirichlet boundary conditions. The new results obtained using this solution are as follows: first, the vessel-vessel heat transfer rate can be a large fraction of the total heat transfer rate of each vessel, thus quantitatively demonstrating the need to accurately model the vessel-vessel heat transfer for vessels imbedded in tissues. Second, the vessel—vessel heat transfer rate is shown to be independent of the source term; while the heat transfer rates from the vessels to the tissue show a significant dependence on the source term. Third, while many previous studies have assumed that (1) the total heat transfer rate from vessels to tissue is zero, and/or (2) the heat transfer rates from paired vessels (of different sizes and at different temperatures) to tissue are equal to each other the current analysis shows that neither of these conditions is met. The analytical solution approach used to solve this two vessels problem is general and can be extended for the case of "N" arbitrarily located vessels.
机译：逆流（容器-容器）传热被认为是生命系统中最重要的传热机制之一。然而，令人惊讶的是，在有限的，未加热/受热的组织区域具有非绝缘边界条件的最一般和重要的情况下，从未进行过对血管，血管和组织的传热速率的准确定量。为了量化这些传热速率，通过求解具有一致Dirichlet边界条件的二维Poisson方程，可以得出温度场的精确解析表达式。使用该解决方案获得的新结果如下：首先，容器-容器的传热速率可能是每个容器的总传热速率的很大一部分，因此定量地证明了需要对以下情况进行精确建模的容器-容器传热血管嵌入组织中。其次，显示出容器-容器的传热速率与源项无关。从血管到组织的热传递速率显示出对源项的显着依赖。第三，尽管许多先前的研究假设（1）从血管到组织的总传热率为零，和/或（2）从成对的血管（大小不同且在不同温度下）到组织的传热率相等彼此之间的当前分析表明，这两个条件都不满足。用于解决这两个船只问题的分析解决方案是通用的，可以扩展到任意放置“ N”个船只的情况。

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