Thermal conductivity in spherical and circular inclusion composites with highly- and lowly-conducting imperfect interfaces

Abstract

The variational three-point correlation results are specified to the problem of conductivity of doubly-coated sphere (circle) assemblage. Limiting procedure is developed to deduce the respective explicit expressions, to calculate and analyse the macroscopic conductivity and the microscopic thermal fields in the assemblages with highly- and lowly-conducting imperfect interfaces under the imposed averaged temperature gradient or averaged flux fields, in comparisons with numerical results for some periodic and random micro-geometries of imperfectly-coated inclusions reported in the literature. Equivalent-inclusion approach based on comparisons of analytical dilute results is combined with available effective medium approximations to extend the results for other typical composites with additional three-point correlation information about their micro-geometry, and the complex mixtures. The theoretical models are also correlated with some available experimental data.