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首页> 外文期刊>International Journal of Heat and Mass Transfer >An analytical derivation of source term dependent, 2-D 'generalized Poisson conduction shape factors'
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An analytical derivation of source term dependent, 2-D 'generalized Poisson conduction shape factors'

机译：源项相关的二维“广义泊松传导形状因子”的解析推导

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摘要

This paper presents derivations for new "generalized Poisson conduction shape factors" (GPCSFs), that are more general than the commonly used conduction shape factors since they include the effects of both source terms and arbitrary, spatially variable boundary temperatures. The GPCSFs are derived for a single, circular vessel eccentrically imbedded in a uniformly heated, homogeneous, circular tissue matrix. Two GPCSF formulations are presented, as based on the difference between the average vessel wall temperature and; (1) the average tissue boundary temperature (S{sub}(tb)), or (2) the average tissue matrix temperature (S{sub}(tm)). The results show first, that the presence of a source term significantly affects the GPCSFs for all vessel radii and eccentricities. Second, unlike standard shape factors with uniform boundary temperatures, the GPCSFs are a function of both the magnitude and distribution of the boundary temperatures; however, these effects are significant only for large vessel radii and eccentricities. Finally, when the vessel cools the tissue, the average tissue matrix temperature GPCSFs are much less sensitive to the source term than are the tissue boundary temperature GPCSFs.
机译：本文介绍了新的“广义泊松传导形状因子”（GPCSF）的派生，它们比常用的传导形状因子更通用，因为它们包括源项和空间可变的任意边界温度的影响。 GPCSF源自偏心地嵌入均匀加热的均匀圆形组织基质中的单个圆形容器。根据平均血管壁温度与温度之间的差异，提出了两种GPCSF配方。 （1）平均组织边界温度（S {sub}（tb）），或（2）平均组织基质温度（​​S {sub}（tm））。结果首先表明，源项的存在会显着影响所有血管半径和偏心距的GPCSF。第二，与具有均匀边界温度的标准形状因子不同，GPCSF是边界温度的大小和分布的函数。但是，这些影响仅对于大的容器半径和偏心率才有意义。最终，当血管冷却组织时，平均组织基质温度GPCSF对来源项的敏感性远低于组织边界温度GPCSF。

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