Prediction of effective thermal conductivity of multiphase composites with periodic microstructures using an expanded micromechanical model

Abstract

Most of the available approaches for the prediction of effective thermal conductivity of composites are proposed for two-phase cases with inhomogeneities of simple geometry. Here, a procedure originally developed for two-phase composites is extended to obtain effective thermal conductivities of periodic composites with an arbitrary number of phases and geometric shapes of the inhomogeneities. The procedure is based on a generalization of the equivalent inclusion method for steady-state heat conduction, using Fourier series to represent the periodic fluctuating fields of the quantities involved in the problem. Applications to three-phase composites with different microstructural features are presented and discussed in detail. The model predictions are compared with analytical and numerical results obtained from other homogenization procedures, as well as with available experimental data. These comparisons show a very good performance of the model regardless of the volume fraction of the inhomogeneities, enabling it to be presented as an interesting alternative to the limited number of existing approaches for evaluating the effective thermal conductivity of multiphase/multi-inclusion periodic composites.