A new model for predicting the thermal conductivities of a composite with spherical microballoons is proposed and consists of two consecutive procedures, the computation of the thermal conductivity of the microballoon and the composite. The microballoon is first replaced by the equivalent filler of a known thermal conductivity, so the composite is treated as the matrix containing the equivalent fillers and its thermal conductivity is derived by using Eshelby model modified with Mori-Tanaka's mean field approach. The present model is validated comparing the predicted, experimental, and numerical results from the literature. Parametric studies in terms of the microballoon volume fraction, its relative wall thickness, and the thermal conductivity ratio of the shell to the matrix have been made and their results are discussed.

In this study, a new model to predict the thermal conductivity of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction by successively embedding small filler volume fraction. The predicted results by the present model are compared with bounds such as parallel, series, and Hashin-Shtrikman models, results by modified Eshelby model, generalized self-consistent model, and effective medium theory, and the experimental results from the literature. It is found that the present model always lies between the bounds and shows better agreement with the experimental results than the other models for various filler volume fractions and thermal conductivity ratios.

Effective thermal conductivity of three-phase composites, consisting of matrix and two kinds of spherical inclusions, has been derived as an explicit form by extending modified Eshelby model (MEM) for two-phase composites. The present results are compared with those by differential effective medium model (DEMM), which are also compared with the experimental results of two-and three-phase composites in the literatures to be validated. For two-phase composites, the results by MEM are better than those by DEMM for the inclusion volume fraction smaller than 0.5. Comparisons between the results by two models and experimental results have been made for three-phase composite, resulting in that MEM predicts better than DEMM for smaller volume fraction of the inclusion having larger inclusion-to-matrix thermal conductivity ratio, but DEMM predicts better as its volume fraction increases. It has been observed through parametric study that its volume fraction is the critical factor affecting the deviation of predictions by the two models. The results by them show a good agreement with the three-phase composite proposed by Molina et al..

An examination of the concept of a microgeometry proposed by Benveniste reveals that the thermal conductivity of the concentric sphere adopted by generalized self-consistent model (GSCM) is equal to that of the composite. It is also noted that the thermal conductivities of the composite with spherical fillers predicted by GSCM and modified Eshelby model (MEM) are the same. These equivalencies enable to propose a simple and alternative approach for determining the thermal conductivity of the composite with multiply coated spherical fillers by applying MEM repeatedly. The present result is compared and shows the exact agreement with the results from literatures.

A closed-form solution using the actual distribution of the fiber aspect ratio is proposed for predicting the stiffness of aligned short fiber composite. The present model is the simplified form of Takao and Taya's model and the extended version of Taya and Chou's model, where Eshelby's equivalent inclusion method modified for finite fiber volume fraction is employed. The validity of using average fiber aspect ratio for predicting the composite stiffness is justified in terms of the scatter of fiber aspect ratio, fiber volume fraction, and constituents' Young's modulus ratio, comparing with the results by the present model. The guideline for selection of either the actual distribution or the average fiber aspect ratio is presented for the better prediction of the composite stiffness.