A mathematical model for thermal conductivity of homogeneous composite materials

Abstract

In this paper, a mathematical model to find the thermal conductivity of a large category of polymer homogeneous composite materials is performed. This type of composites contains ideal spherical particles encircled by an inhomogeneous interphase region, whereas the matrix is considered as isotropic. The thermal conductivity of the interphase is formulated as a continuous single-valued function of the radius of a spherical model. In this context, it is evident that the concept of boundary interphase is a useful manner for a quantitative description of the adhesion efficiency between matrix and filler since it is well known that there is a considerable effect of this phase on the thermo-mechanical properties of the composite. On the other hand, the particle distribution which can be considered as the influence of neighboring particles and their possible interaction should affect the thermal conductivity of the overall material.