Application of Eshelby's tensor and rotation matrix for the evaluation of thermal transport properties of composites

Many applications in the electronic industry require an optimum combination of thermal transport properties (e.g., high thermal conductivity for a given coefficient of thermal expansion). This combination cannot possibly be obtained using a single material and hence requires judicious selection of matrix material with appropriate distribution of the second phase to form a composite. Such a composite provide the combination of thermal properties required for a given application. The properties of matrix and reinforcing materials, as well as shape, size and relative volume fraction and spatial distribution of the reinforcing phase, all play key roles in determining the overall thermal properties of the composite. In this work, we present an analytical model based on Eshelby's tensor for determining the coefficient of thermal expansion (a) and thermal conductivity (k) of composites. We are able to account for the effect of different fiber shapes and volume fractions; in addition, we have included the effect of orientation distribution of the fibers (inhomogeneities) on the composite thermal properties. The calculated values compare favorably with the available experimental data.