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Materials 2012, 5(3), 528-539; doi:10.3390/ma5030528

Article

Exact Solution of a Constraint Optimization Problem for the Thermoelectric Figure of Merit

Wolfgang Seifert ^1,*  and Volker Pluschke ²

¹ Institute of Physics, University Halle-Wittenberg, Halle D-06099, Germany ² Institute of Mathematics, University Halle-Wittenberg, Halle D-06099, Germany

* Author to whom correspondence should be addressed.

Received: 13 January 2012; in revised form: 15 March 2012 / Accepted: 19 March 2012 / Published: 21 March 2012

(This article belongs to the Special Issue Advances in Functionally Graded Materials)

Download PDF Full-Text [158 KB, Updated Version, uploaded 22 March 2012 15:24 CET]

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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.

Keywords: thermoelectricity; functionally graded material; figure of merit; device optimization

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