The distribution of the temperature and heat flux fields around a couple of unequal nonconductive tangent spherical inhomogeneities (or pores) embedded in an infinite medium under a steady-state and remotely applied heat flux is addressed in the present work. Owing to the 3D geometrical layout of the inhomogeneity, use is made of the tangent sphere coordinate system. A corrective temperature field expressed in terms of convergent integrals is superposed to the fundamental one to fulfill the BCs at the surfaces of the spheres. When the heat flux is aligned to the symmetry axis (axisymmetric problem), the solution can be found straightforwardly by introducing a stream function, which allows for transforming the Neumann BCs into a Dirichlet boundary value problem. Conversely, for the transversal heat flux (non-axisymmetric problem), the problem is formulated in terms of temperature, thus leading to a system of two ODEs which is handled numerically through a Euler shooting method, after preliminary asymptotic expansions. Once the temperature fields are known, the components of the resistivity contribution tensor are assessed varying the aspect ratio of the two spheres. It is found that the extrema of the thermal resistivity are achieved for spheres of equal size. The study allows assessing the effective thermal conductivity of a wide range of smart composites involving insulating inhomogeneities resembling sphere doublets.

在目前的工作中，解决了在稳态和远程应用热通量下嵌入无限介质中的一对不相等的非导电切线球形不均匀性（或孔隙）周围的温度和热通量场分布。由于不均匀性的 3D 几何布局，使用了切球坐标系。用收敛积分表示的校正温度场叠加到基本场上，以实现球体表面的 BC。当热通量与对称轴对齐（轴对称问题）时，可以通过引入流函数直接找到解决方案，这允许将 Neumann BC 转换为 Dirichlet 边值问题。相反，对于横向热通量（非轴对称问题），这个问题是根据温度来表述的，因此导致了一个由两个 ODE 组成的系统，在初步渐近展开之后，通过欧拉射击方法进行数值处理。一旦温度场已知，电阻率贡献张量的分量就会通过改变两个球体的纵横比来评估。发现对于相同尺寸的球体，达到了热阻率的极值。该研究允许评估各种智能复合材料的有效导热率，这些复合材料涉及类似于球双联体的绝缘不均匀性。电阻率贡献张量的分量是通过改变两个球体的纵横比来评估的。发现对于相同尺寸的球体，达到了热阻率的极值。该研究允许评估各种智能复合材料的有效导热率，这些复合材料涉及类似于球双联体的绝缘不均匀性。电阻率贡献张量的分量是通过改变两个球体的纵横比来评估的。发现对于相同尺寸的球体，达到了热阻率的极值。该研究允许评估各种智能复合材料的有效导热率，这些复合材料涉及类似于球双联体的绝缘不均匀性。