Maximum cooling power of a graded thermoelectric cooler

Gerstenmaier and Wachutka [Phys. Rev. E 86, 056703 (2012)] have published a new approach to optimizing the material grading in thermoelectric converters by means of a generalized Lagrange multiplier method. A detailed analysis of this method reveals that maximization of the cooling power of a graded thermoelectric cooler with fixed length requires a separate consideration as an optimal control problem. Referring to an ideal single-element device the mathematical analysis presents optimal Seebeck profiles with a singularity at the element's hot side, depending on the temperature profile under consideration. Based on these optimal profiles the corresponding maximum of the absorbed thermal power (cooling power) is discussed. The new findings are compared to results obtained for constant material properties and equivalent figure of merit. It is shown that a performance improvement regarding cooling power by a factor of 2 or more can theoretically be achieved by an optimal material grading. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim