The influence of spherical inclusions on the effective thermoelectric properties of thermoelectric composite materials

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. 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 materials containing spherical inclusions can be higher than that of each constituent in the absence of size and interface effects. Some interesting examples of actual thermoelectric composites with spherical inclusions, such as insulated cavities, inclusions subject to conductive electric and heat exchange and thermoelectric inclusions, are considered, numerical results lead to the conclusion that considerable enhancement of the effective figure of merit can be achievable by introducing inclusions. This paper provides a theoretical foundation for analytical and computational treatments of thermoelectric composites with more complicated inclusion structures, and thus points to a new route for their design and optimization.