Numerical performance estimation of segmented thermoelectric elements

Functionally graded and segmented thermoelements have been considered for long, aiming at improving the performance of thermogenerators (TEG) which are exposed to a large temperature difference. A numerical algorithm has been previously developed using the software MATHEMATICA and has been applied for modelling homogeneous and segmented Peltier elements. It is capable to calculate the exact temperature profile along a segmented element in a one-dimensional model. The algorithm is based on the constant properties assumption (CPA) in each of the segments and is also providing the opportunity of treating quasi-continuous gradients. Integral quantities like the voltage drop over the element and performance parameters like cooling power and C.O.P. (for a Peltier cooler) or output power and efficiency (for a TEG) are deduced taking into account the real temperature dependence of the materials properties. This algorithm was inserted in a loop (varying the current density) to determine optimum operation parameters at given temperature difference. Numerical parameter studies based on quasi-continuously grade elements, CPA in each of the segments, and preassuming constant volume average of the figure of merit over the whole element (ZT) provide guidelines for advantageous TE gradients in Peltier coolers and TEG. A practical example is illustrating the quantitative improvement of performance achievable by segmentation of a Peltier cooler.