Linking electrical and thermal conductivity through cross-property inclusion modelling

TL;DR

This paper introduces a new differential effective medium model linking electrical and thermal conductivities in composites, validated by experiments on copper-graphite materials, and highlights its independence from volume fraction and dependence on inclusion shape.

Contribution

It presents a novel cross-property differential effective medium scheme that models thermal and electrical conductivities simultaneously, considering inclusion aspect ratio and validated with experimental data.

Findings

Successfully models laboratory measurements on copper-graphite composites

Inferred aspect ratio matches physical inclusion shape

Scheme is independent of inclusion volume fraction

Abstract

We derive a new cross-property differential effective medium scheme for a composite material's thermal conductivity as a function of its electrical conductivity and vice versa. Our scheme assumes that one phase is embedded in the other as inclusions. The relations are independent of inclusion volume fraction, but depend on the aspect ratio of the inclusions. We show that the method successfully models published laboratory measurements on a copper-graphite composite, with the inferred aspect ratio matching the physical shape of the inclusions. This work complements earlier results on elastic-electrical cross-property differential effective medium modelling, and has the potential to be extended for different cross-property relationships.