Finite element analysis and material sensitivity of Peltier thermoelectric cells coolers

In this work, a finite element simulation of a commercial thermoelectric cell, working as a cooling heat pump, is presented. The specially developed finite element is three-dimensional, non-linear in its formulation (using quadratic temperature-dependence on material properties) and fully coupled, including the Seebeck, Peltier, Thomson and Joule effects. Another special interface finite element is developed to prescribe the electric intensity, taking advantage of repetitions and symmetries. A thorough study of the distributions of voltage, temperature and the corresponding fluxes is presented, and the performance of the cell is compared with that of the manufacturer and with simplified analytical formulations, showing a good agreement. Combining the finite element model with the Monte Carlo technique, a sensitivity analysis is presented to take into account the performance dependence on the material properties, geometrical parameters and prescribed values. This analysis, which can be considered a first step to optimize these devices, concludes that the temperature-dependence of the material properties of electric conductivity and Seebeck coefficient is very relevant on cell performance.