OPTIMIZATION OF VARIABLE CROSS-SECTIONAL AREA THERMOELECTRIC ELEMENTS THROUGH MULTI-METHOD THERMAL-ELECTRIC COUPLED MODELING

Abstract

A well-posed thermal-electric coupled mathematical-numerical model to optimize the cross-sectional area per length of a thermoelectric (TE) leg is introduced to maximize thermal conversion efficiency ( η ) or power output ( P o ). To employ such optimization, the p - or n -type leg was divided into uniform length segments, wherein the product of the electrical resistance ( R el ) and thermal conductance ( K ) was minimized as to maximize the figure of merit ( ZT ) of each individual partition. The minimization of R el K was dependent upon the temperature difference established across each segment, which was resolved using a one-dimensional finite difference (FD) scheme of the TE general energy equation (GEQ). The TE GEQ included all pertinent phenomena —conduction, Joule, Peltier and Thomson effects —as well as temperature dependent properties. The boundary conditions of the FD scheme were provided via a one-dimensional thermal resistance network. The current output of the unicouple was determined by the temperature bounds across the junction and the internal resistance of the TE legs, and this was explicitly coupled to the TE GEQ to create a fully-coupled model. The proposed model was validated to a fully-coupled thermal-electric finite volume method model implemented in ANSYS CFX. The proposed optimization process yielded improvements in volumetric efficiency and volumetric power output of 4.60% and 3.75%, respectively, in comparison to conventional constant-area optimization processes.