Effective thermal conductivity of functionally graded composite with arbitrary geometry of particulate

In this paper, a new micromechanical method, the Weighted Residual Self-consistent Scheme (WRSCS), is developed for the prediction of the effective thermal conductivity of particulate composites with arbitrary configurations. The method is based on the concept of the traditional Self-consistent Scheme (SCS). For some special configurations of inclusions, such as spherical or ellipsoidal, the effective conductivity of the composite can be solved without much difficulty using SCS. But for the composite with inclusion of arbitrary geometry, such as polygon or other irregular configurations, it is difficult to get an analytic solution. In the WRSCS, the arbitrary inclusion configuration is modeled by applying collocation points at interface. Based on SCS micromechanical model, the local fields inside the inclusion can be evaluated by using the solution of a single inclusion in an infinite matrix and inclusion interaction is taken into account through the yet unknown average equivalent medium. The solution for calculating the potential field inside the inclusion is obtained by means of Weighted Residual Method (WRM). Using the WRSCS, the effective thermal conductivities for composites with different inclusion's geometry are calculated. For the case of spherical inclusion, the results from the WRSCS show good agreements with the one from traditional SCS [7, 8]. Examining results corresponding to different inclusion's geometry, it shows that the effective thermal conductivity depends not only on the volume fractions and the properties of components, but also on the inclusion's configuration.