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首页> 外文期刊>International Journal of Heat and Mass Transfer >An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions
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An analytical study of heat transfer in a finite tissue region with two blood vessels and general Dirichlet boundary conditions

机译：具有两个血管和一般Dirichlet边界条件的有限组织区域中的传热分析研究

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摘要

Vessel-vessel and vessel-tissue heat transfer rates are defined and explicitly quantified, for the first time, for a uniformly heated, finite, circular tissue region with two arbitrarily imbedded circular vessels and general Dirichlet boundary conditions. These heat transfer rates are obtained using an exact analytical solution for the tissue temperature field that is derived herein. Based on these heat transfer rates two different types of Poisson conduction shape factors (PCSFs) are defined. One is related to the vessel-vessel heat transfer rate (VVPCSF) and the other is related to the vessel-tissue heat transfer rates (VTPCSF). Two, conventional, alternative formulations for the VTPCSFs are studied; one is based on the difference between the average vessel wall and tissue boundary temperatures, and the other on the difference between the average vessel wall and the average tissue matrix temperatures. The effects of the angularly varying, non-uniform boundary conditions, the source term and the diameters and locations of the two vessels on these heat transfer rates and PCSFs are studied for the typical case of vessels cooling a tissue; i.e., when the average vessel wall boundary temperatures are lower than the average tissue boundary temperature. Results show that first, the effects of vessel wall temperature fluctuations on both the vessel-vessel and the vessel-tissue heat transfer rates are significant. Second, unlike the vessel wall temperature fluctuations, fluctuations at the outer tissue boundary affect only the vessel-tissue heat transfer rates. They do not affect the vessel-vessel heat transfer rates. Third, when strong fluctuations are present on the vessel walls and outer tissue boundary the shape factors are dependent on the shape of the fluctuations, and are thus very problem specific. Further, the analytical solution procedure used to derive the solution for the temperature field and the methodology developed to quantify the heat transfer rates are general and can be extended for the case of 'N' arbitrarily located vessels.
机译：首次定义并明确量化了均匀加热的，有限的圆形组织区域（具有两个任意嵌入的圆形容器和一般Dirichlet边界条件）的容器-容器和容器-组织的传热速率。这些传热速率是使用针对本文得出的组织温度场的精确分析溶液获得的。基于这些传热速率，定义了两种不同类型的泊松传导形状因子（PCSF）。一个与血管-血管传热速率（VVPCSF）有关，另一个与血管-组织传热速率（VTPCSF）有关。研究了VTPCSF的两种常规替代配方；一种基于平均血管壁和组织边界温度之间的差异，另一种基于平均血管壁和平均组织基质温度之间的差异。对于容器冷却组织的典型情况，研究了角度变化，边界条件不均匀，源项以及两个容器的直径和位置对这些传热速率和PCSF的影响。即，当平均血管壁边界温度低于平均组织边界温度时。结果表明，首先，脉管壁温度波动对脉管和脉管-组织传热速率的影响都是显着的。其次，与血管壁温度波动不同，组织外部边界处的波动仅影响血管组织的传热速率。它们不影响容器的传热速率。第三，当在血管壁和外部组织边界上存在强烈的波动时，形状因数取决于波动的形状，因此非常有针对性。此外，用于导出温度场解决方案的分析解决方案程序和开发用于量化传热速率的方法是通用的，可以扩展到“ N”个任意放置的容器的情况。

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