Influence of spherical inclusions on effective thermoelectric properties of thermoelectric composite materials**Project supported by the Ningbo Natural Science Foundation, China (Grant Nos. 2019A610151 and 2018A610081), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LY17A020001 and LY20A020002), the National Natural Science Foundation of China (Grant No. 11402063), and the K C Wong Magna Fund in Ningbo University, China.

Abstract

A homogenization theory is developed to predict the influence of spherical inclusions on the effective thermoelectric properties of thermoelectric composite materials based on the general principles of thermodynamics and Mori–Tanaka method. The closed-form solutions of effective Seebeck coefficient, electric conductivity, heat conductivity, and figure of merit for such thermoelectric materials are obtained by solving the nonlinear coupled transport equations of electricity and heat. It is found that the effective figure of merit of thermoelectric material containing spherical inclusions can be higher than that of each constituent in the absence of size effect and interface effect. Some interesting examples of actual thermoelectric composites with spherical inclusions, such as insulated cavities, inclusions subjected to conductive electric and heat exchange and thermoelectric inclusions, are considered, and the numerical results lead to the conclusion that considerable enhancement of the effective figure of merit is achievable by introducing inclusions. In this paper, we provide a theoretical foundation for analytically and computationally treating the thermoelectric composites with more complicated inclusion structures, and thus pointing out a new route to their design and optimization.