Numerical Modeling of Leg Geometries in Thermoelectric Devices
Open AccessGlobal energy consumption is large and has increased rapidly over recent years. According to International Energy Agency, global energy demand rose by 2.3% in 2018, which marks the fastest pace in the last decade. Wasted energy is a big fraction of the overall energy consumed globally. This large fraction of wasted energy highlights the need to reduce or recycle waste energy, which otherwise would not fulfill any further energy needs. Thermoelectric devices have the potential to improve energy efficiency because they can convert wasted heat into electrical energy. Thermoelectric devices consist of two ceramic plates, between which are legs of semiconductor thermoelectric material, commonly bismuth telluride. Hence, thermoelectric legs are the main constituents of the thermoelectric devices. Thermoelectric legs are required to have low electrical resistance and high thermal resistance for a best performance. Both electrical resistance and thermal resistance are dependent on the materials and on the geometry of the legs, especially the length of the legs and the cross-sectional area. Additive manufacturing enables production of complex geometries with different shapes than current commercially available uniform legs. This work focused on understanding the effect of different thermoelectric leg designs on thermoelectric device performance. Various leg geometries were studied for their thermal and electrical performance under different boundary condition scenarios. The shapes studied include rectangular prisms, trapezoids, hourglass and Y shapes. Two numerical studies were performed. In the first, the temperature gradients in the thermoelectric legs are determined by solving for the energy balance equation. This is done by using a code written in Python. In the second, temperature gradients and the electrical potentials of the thermoelectric legs are determined using the COMSOL-Multiphysics Thermoelectric Module. The models include geometries in which the cross section of the legs vary along their height. Such geometries enable better understanding of the contribution of cross section area changes on the thermal and electrical performance. Both fixed temperature and fixed heat flux boundary conditions were examined numerically. It is found that different boundary conditions, which reflect different working environments, result in different performance values for the same leg shapes. 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 shape leg enabled a 101% bigger electrical potential and a 254% greater maximum power compared to the original rectangular shape under constant temperature boundary condition. The inverse hourglass performed 23% better for electrical potential and 43% better for maximum power compared to the original rectangular shape under heat flux boundary condition. These findings underscore the importance of geometry upon electrical and thermal performance of a thermoelectric leg, as well as the importance of selecting the best shape with respect to the working environment.
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