Generalized Heat Equation and the Influence of the Leg Geometry on the Performance of a Thermoelectric Element

Kurzfassung

Recently thermoelectricity as a direct energy conversion technology gained a lot of interest. The long known physical effects of thermoelectricity can be applied in solid-state devices, e.g. as thermoelectric generator (TEG) which converts heat into electricity or as a thermoelectric cooler (TEC) in which an electrical current is used to produce a temperature difference. There are several potential applications of thermoelectric power generation, such as waste heat recovery in energy conversion systems, industrial processes or in automotive applications. The performance of a thermoelectric (TE) device depends on various factors besides the material properties which are a focus research target in investigations of thermoelectrics nowadays. Key factors influencing the performance are the working conditions like the junction temperatures and/or heat fluxes, contacting of the TE material to a metal bridge. In this work we want to focus on the influence of the geometry or the topology of a TE element on the performance of a TE device. The framework of the investigation is delivered by the Onsager-deGroot-Callen theory, a kind of field theory in thermoelectricity which provides a thermal energy balance. A literature review shows that up to now the investigations on TE devices with shaped elements are done mostly in a one-dimensional setup. Obviously it is clear that if the TE elements are shaped (non-prismatic, non-cylindrical), the problem is a priori at least two-dimensional. To investigate the influence of the shape the generalized heat balance within the constant properties material approximation is solved with different techniques. First of all the standard quasi-1D calculation which can be done analytically is reviewed. Afterwards a truncated cone as a 2D axisymmetric problem is observed and the impact on the performance highlighted. Arbitrary shapes can be examined with the finite element method (FEM) a numerical method. This method is used to verify the results from the analytical and approximative solutions.