A nonlocal theory for the heat transport in composites containing highly conducting fibrous inclusions
A nonlocal theory for the heat transport in composites containing highly conducting fibrous inclusions
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含有高导热纤维夹杂物的复合材料中热传输的非局域理论
DOI：
10.1063/1.866594
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发表时间：
1988
影响因子：
4.6
通讯作者：
E. Shaqfeh
中科院分区：
文献类型：
--
作者：
E. Shaqfeh
本文提出了一种理论来描述含有高导电性纤维夹杂物的复合材料在平均温度场与所含纤维长度相当的条件下的传热。因此，与以前的发展相比，这种纤维可以对快速变化的温度场的细节进行采样，而不是简单地对局部线性场进行采样。利用平均方程和细长体理论的方法，证明了纤维的存在所产生的平均“额外通量”是任意点的温度梯度的积分，该温度梯度由适当的非局部电导率函数加权。这种材料中的热传递的表示明确适用于(a)稀复合材料，其中nf l3≪1，其中nf是纤维的密度，l是纤维的长度；(b) nfl3 < 1但nflb2 < 1的半稀复合材料，其中b为纤维厚度。在这两种情况下，推导出的表达式对……严格有效。
A theory is developed to describe the heat transfer in composites containing highly conducting fibrous inclusions under conditions in which the average temperature field scales on lengths comparable to the length of the included fibers. Thus, in contrast to previous developments, the fiber samples the details of a rapidly varying temperature field rather than simply a local linear field. Using the method of averaged equations and slender body theory, the average ‘‘extra flux’’ created by the presence of the fibers is demonstrated to be an integral of the temperature gradient about any point weighted by a function which is the appropriate nonlocal conductivity. This representation of the thermal transport in the material is derived explicitly for (a) dilute composites in which nf l3≪1, where nf is the number density of the fiber and l is their length; and (b) semidilute composites in which nfl3≫1 but nflb2≪1, where b is the fiber thickness. In both instances the expressions derived are rigorously valid for...