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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

1,*  and 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 / Revised: 15 March 2012 / Accepted: 19 March 2012 / Published: 21 March 2012
(This article belongs to the Special Issue Advances in Functionally Graded Materials)
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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 thermoelectricity; functionally graded material; figure of merit; device optimization
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Seifert, W.; Pluschke, V. Exact Solution of a Constraint Optimization Problem for the Thermoelectric Figure of Merit. Materials 2012, 5, 528-539.

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