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 TVT, 2002, Volume 40, Issue 2, Pages 323–327 (Mi tvt1783)

Heat and Mass Transfer and Physical Gasdynamics

Extremum Principles in the Theory of Thermal Conductivity of a Solid

A. S. Pleshchanov

"Krzhizhanovsky Power Engineering institute"

Abstract: It is shown that the principle of minimum of entropy production under steady-state conditions is correct for one-dimensional geometry at arbitrary temperature dependences of thermal conductivity and specific heat in some region of values of these coefficients rather than only at a concrete dependence of thermal conductivity in the principle formulation. However, in this case, in view of the absence of a variational description, it is only possible to investigate the validity of just the necessary condition of the principle correctness. In view of this, another variational principle is suggested, which is defined as the principle of minimum algebraic sum of squares of dissipative flows and is free of the defects of the first principle.

Full text: PDF file (914 kB)

English version:
High Temperature, 2002, 40:2, 295–299

Bibliographic databases:

UDC: 536.75 : 539.2

Citation: A. S. Pleshchanov, “Extremum Principles in the Theory of Thermal Conductivity of a Solid”, TVT, 40:2 (2002), 323–327; High Temperature, 40:2 (2002), 295–299

Citation in format AMSBIB
\Bibitem{Ple02} \by A.~S.~Pleshchanov \paper Extremum Principles in the Theory of Thermal Conductivity of a Solid \jour TVT \yr 2002 \vol 40 \issue 2 \pages 323--327 \mathnet{http://mi.mathnet.ru/tvt1783} \transl \jour High Temperature \yr 2002 \vol 40 \issue 2 \pages 295--299 \crossref{https://doi.org/10.1023/A:1015271727422} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000175472200022} 

• http://mi.mathnet.ru/eng/tvt1783
• http://mi.mathnet.ru/eng/tvt/v40/i2/p323

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Hua Yu.-Ch., Guo Z.-Yu., “The Least Action Principle For Heat Conduction and Its Optimization Application”, Int. J. Heat Mass Transf., 105 (2017), 697–703
2. Hua Yu.-Ch., Zhao T., Guo Z.-Yu., “Irreversibility and Action of the Heat Conduction Process”, Entropy, 20:3 (2018), 206
3. A. G. Vikulov, A. V. Nenarokomov, “Refined solution of the variational problem of identification of lumped parameter mathematical models of heat transfer”, High Temperature, 57:2 (2019), 211–221