Effective behaviors of anisotropic thermoelectric composites containing ellipsoidal inclusions

Thermoelectric (TE) materials are well-known to be able to directly convert heat into electricity. In developing high-performance TE materials, the inclusions are often used to enhance its energy conversion efficiency. In this paper, an effective medium model is developed to evaluate the effective behaviors of anisotropic TE composites containing multiple inclusions. First, the non-linearly coupled TE governing equations are solved by defining two generalized field variables. Then, the effective TE properties are derived based on the fundamental idea of Eshelby's theory and the self-consistent method, and the explicit solutions for some particular inclusion cases are given. Furthermore, the presented models are validated by finite element simulations and the effects of inclusion properties and inclusion shapes on the performance of the TE composite are discussed. The results show that specific inclusions may greatly boost the TE figure of merit of the composite. Furthermore, we apply the presented model to a commercial thermoelectric cooler(TEC) module, and find that the cooling performance can be enhanced by as much as 22.79% by inserting voids. The presented research thus sheds considerable insight into the performance evaluation of effective behavior of TE composites and may pave a new way of boosting the performance of TE devices.