含稀疏分布杂质的复合材料中的均匀化稳恒热传导方程

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Homogenized Equations for Steady Heat Conduction in Composite Materials with Dilutely Distributed Impurities

摘要: 本文应用双空间尺度法导出了含稀疏分布椭圆柱形杂质的复合材料柱中的均匀化稳恒热传导方程,求得了等效导热系数的具体形式,并指出,当杂质枉截面单向分布时,宏观热传导是各向异性的,而当杂质枉截面按方向均匀分布时,宏观热传导是各向同性的.

Abstract: In this paper, by using the two-space method, homogenized equations for steady heat conduction in the composite material cylinders with dilutely-distributed elliptic cylinders of impurities are derived, and the explicit expressions for the corresponding effective heat conductivity of those which are concerned are obtained. It is also shown that the macroscopic heat conduction is anisotropic when the cross-sections of the impurity cylinders are unidliec-tionally oriented and isotropic when the angular distribution of the cross-sections is uniform.

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