Graded and stacked thermoelectric generators—numerical description and maximisation of output power

Abstract

Large temperature differences applied to thermoelectric generators require that the variations of all material properties with temperature are included in a numerical description of their performance. A finite element algorithm is developed to calculate the temperature field in a thermoelectric device and concomitantly its thermoelectric performance under operation conditions. Spatially varying the composition of material or the doping concentration allows to enhance the power output or efficiency. The choice of the optimum concentration parameter profiles is shown not to be a function of the local temperature only, but to be dependent on a local criterion related to the entire temperature field. This criterion is included in an iterative calculus to find optimised concentration profiles. It is shown that the code developed has advantages over previously published solutions, since it can be applied to continuous and discontinuous material changes without any assumptions on the mutual dependence of the governing transport parameters or a need to cast their temperature dependence into analytical form. The performance is shown for some test situations and compared to literature.