Effective thermal conductivity in thermoelectric materials

Thermoelectric generators (TEGs) are solid state heat engines that generate electricity from a temperature gradient. Optimizing these devices for maximum power production can be difficult due to the many heat transport mechanisms occurring simultaneously within the TEG. In this paper, we develop a model for heat transport in thermoelectric materials in which an "effective thermal conductivity" (κ eff) encompasses both the one dimensional steady-state Fourier conduction and the heat generation/consumption due to secondary thermoelectric effects. This model is especially powerful in that the value of κ eff does not depend upon the operating conditions of the TEG but rather on the transport properties of the TE materials themselves. We analyze a variety of thermoelectric materials and generator designs using this concept and demonstrate that κ eff predicts the heat fluxes within these devices to 5% of the exact value.