Abstract The problem about steady-state temperature distribution in a homogeneous isotropic medium containing a pore or an insulating inhomogeneity formed by two coalesced spheres of the same radius, under arbitrarily oriented uniform heat flux, is solved analytically. The limiting case of two touching spheres is analyzed separately. The solution is obtained in the form of converged integrals that can be calculated using Gauss-Laguerre quadrature rule. The temperature on the inhomogeneity's surface is used to determine components of the resistivity contribution tensor for the insulating inhomogeneity of the mentioned shape. An interesting observation is that the extreme values of these components are achieved when the spheres are already slightly coalesced.

中文翻译：

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球形孔聚结对材料整体电导率的影响。

摘要 解析解决了在任意取向的均匀热通量下，含有孔隙或绝缘不均匀性的均匀各向同性介质中的稳态温度分布问题，该介质由具有相同半径的两个聚结球体形成。分别分析了两个接触球体的极限情况。该解以收敛积分的形式获得，可以使用 Gauss-Laguerre 求积法则计算。不均匀性表面上的温度用于确定所述形状的绝缘不均匀性的电阻率贡献张量的分量。一个有趣的观察结果是，当球体已经稍微聚结时，就会达到这些分量的极值。