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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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.
AbstractList 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.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.
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.
Author Pluschke, Volker
Seifert, Wolfgang
AuthorAffiliation 1 Institute of Physics, University Halle-Wittenberg, Halle D-06099, Germany
2 Institute of Mathematics, University Halle-Wittenberg, Halle D-06099, Germany
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  surname: Seifert
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  givenname: Volker
  surname: Pluschke
  fullname: Pluschke, Volker
BackLink https://www.ncbi.nlm.nih.gov/pubmed/28817061$$D View this record in MEDLINE/PubMed
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crossref_primary_10_1103_PhysRevApplied_8_064003
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Cites_doi 10.1103/PhysRevLett.91.148301
10.1557/jmr.2011.139
10.1002/pssa.200925460
10.1063/1.1735380
10.3390/e13081481
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Issue 3
Keywords figure of merit
thermoelectricity
device optimization
functionally graded material
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References ref_1
ref_3
ref_2
Seifert (ref_4) 2011; 26
Sherman (ref_10) 1960; 31
ref_9
Goupil (ref_11) 2011; 13
ref_5
Seifert (ref_8) 2010; 207
ref_7
ref_6
14611561 - Phys Rev Lett. 2003 Oct 3;91(14):148301
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  doi: 10.1103/PhysRevLett.91.148301
– volume: 26
  start-page: 1933
  year: 2011
  ident: ref_4
  article-title: Maximum performance in self-compatible thermoelectric elements
  publication-title: J. Mater. Res.
  doi: 10.1557/jmr.2011.139
– volume: 207
  start-page: 760
  year: 2010
  ident: ref_8
  article-title: The compatibility approach in the classical theory of thermoelectricity seen from the perspective of variational calculus
  publication-title: Phys. Status Solidi A
  doi: 10.1002/pssa.200925460
– volume: 31
  start-page: 1
  year: 1960
  ident: ref_10
  article-title: Calculation of efficiency of thermoelectric devices
  publication-title: J. Appl. Phys.
  doi: 10.1063/1.1735380
– volume: 13
  start-page: 1481
  year: 2011
  ident: ref_11
  article-title: Thermodynamics of thermoelectric phenomena and applications
  publication-title: Entropy
  doi: 10.3390/e13081481
– reference: 14611561 - Phys Rev Lett. 2003 Oct 3;91(14):148301
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SubjectTerms Integrals
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Temperature
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