Resistivity contribution tensor for nonconductive sphere doublets

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