Abstract
A nonlinear model of coupled thermoelectricity is presented and implemented in the finite element method. The model accounts for the Seebeck, Peltier and Thomson effects in thermoelectric materials within the framework of the coupled thermal and electrical behaviors governed by the Fourier and Ohm’s laws. The resulting finite element system of equations is expressed directly in terms of the potential variables, i.e. voltage and temperature, and it is solved using the Newton method by formulating the stiffness and Jacobian matrices with respect to these fundamental variables. The model is verified by comparing its predictions with the analytical solution resulting from the system of ordinary differential equations that represent the simplified model for the one-dimensional case. Then, the finite element model is applied to estimate the energy conversion performance of nanostructured thermoelectric materials compared with that of traditional bulk materials. The study illustrates the excellent behavior of nanostructured materials in terms of their power output and conversion efficiency. The analysis shows the advantages of developing nanostructured thermoelectric materials for increased performance and miniaturization.