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

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 ma...

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Published inMaterials Vol. 5; no. 3; pp. 528 - 539
Main Authors Seifert, Wolfgang, Pluschke, Volker
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 21.03.2012
MDPI
Subjects
Integrals
Optimization
Temperature
Germany
figure of merit
thermoelectricity
device optimization
functionally graded material
Online AccessGet full text
ISSN1996-1944
1996-1944
DOI10.3390/ma5030528

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Summary: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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ISSN:1996-1944
1996-1944
DOI:10.3390/ma5030528