Stefan Lampenscherf

Fast solution of thermoelectric equation for inhomogeneous devices

Computation speed is important in the optimization of systems which include several TE-modules at different temperatures and el. currents. Typically for maximum power generation or maximum efficiency the individual module currents and leg-lengths in the modules have to be optimized. Also optimization of inhomogeneous material distribution within TE-legs is an issue. This work will demonstrate that by making use of the continuity conditions for heat current and temperature, the general nonlinear problem with position-and temperature-dependent material properties can be solved quickly and precisely in one-dimensional TE-legs. Different algorithms are presented with calculation times of typically 0.2 s on a 3GHz single core PC. The nodal methods presented are robust also in case of material discontinuities, where differential equation solvers can have problems. It is important to include thermal contact resistors to the heat reservoirs in the calculation, which can be done easily by setting the Seebeck S equ...

Rigorous optimization procedure for inhomogeneous thermoelectric converters

The rigorous optimization of thermoelectric (TE) devices with inhomogeneous material properties is still an unsettled problem. With the help of a newly introduced method of generalized Lagrange multiplier functions a solution is presented. The method leads to a coupled system of ordinary differential equations, which can be solved swiftly numerically. That may also be of interest in other branches of physics. For TE-generators the achieved enhancements by optimized thermo-power distribution for constant figure of merit Z are small compared to the uniform case. In the refrigerator mode exists a higher potential for optimization. A drastic increase in the maximum temperature difference is possible at the expense of largely reduced cooling efficiency. It is shown that the maximum TE generator and cooling efficiencies are independent of the thermal conductivity profile, which limits the optimization potential for graded devices.