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Exact Solution of a Constraint Optimization Problem for the Thermoelectric Figure of Merit
Wolfgang Seifert1, Volker Pluschke2
1Institute of Physics, University Halle-Wittenberg, Halle D-06099, Germany. wolfgang.seifert@physik.uni-halle.de.
Abstract:
In the classical theory of thermoelectricity, the performance integrals for a fully self-compatible material depend on the dimensionless figure of merit zT. Usually these integrals are evaluated for constraints z = const. and zT = const., respectively. In this paper we discuss the question from a mathematical point of view whether there is an optimal temperature characteristics of the figure of merit. We solve this isoperimetric variational problem for the best envelope of a family of curves z(T)T.
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