The Influence of Leg Shape on Thermoelectric Performance Under Constant Temperature and Heat Flux Boundary Conditions

Abstract

Global energy resource consumption is increasing rapidly, and wasted energy (the portion not used for useful services) comprises a significant fraction of the energy consumed. Much of the wasted energy is in the form of heat. Thermoelectric devices offer the potential to convert this wasted heat into electricity, and they can be used for thermal management by pumping heat. The shape of thermoelectric devices, particularly the active semiconducting material units (or thermoelectric legs) within the device, has remained largely unchanged. However, the advent of new manufacturing techniques such as additive manufacturing enables customizable device shapes. Given these new manufacturing capabilities, exploring atypical, or non-rectangular, leg geometries becomes increasingly relevant. This work focuses on understanding the effect of different thermoelectric leg designs on thermoelectric device performance. Various leg shapes were studied for their thermal and electrical performance under different thermal boundary conditions. The shapes studied include rectangular prisms, rectangular prisms with interior hollows, trapezoids, hourglass, and Y-shapes. Temperature gradients and the electrical potentials of the thermoelectric legs are determined using the COMSOL Multiphysics Thermoelectric Module. Both fixed temperature and fixed heat flux boundary conditions were examined numerically. Among the geometries investigated, the hourglass-shaped thermoelectric leg, subjected to a fixed temperature boundary condition, is found to have the best thermal and electrical performance. The hourglass-shaped leg results in more than double the electrical potential and maximum power compared to the conventional rectangular shape when the cold side experiences a natural convection boundary condition. Under a fixed heat flux boundary condition on the hot side, a trapezoid-shaped leg results in almost double the electrical potential and a 50% increase in the power output compared to the conventional leg shape. Varying boundary conditions, which reflect different device operating conditions, result in different performance values for the same leg shapes. These findings underscore the importance of leg geometry on electrical and thermal performance of a thermoelectric leg, as well as the importance of considering the device operating condition when selecting the best leg shape.