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Applications of Mathematics

, Volume 58, Issue 4, pp 405–422 | Cite as

Optimal design of the cooling plunger cavity

  • Petr SalačEmail author
Article

Abstract

An axisymmetric system of mould, glass piece, plunger and plunger cavity is considered. The state problem is given as a stationary head conduction process. The system includes the glass piece representing the heat source and is cooled inside the plunger cavity by flowing water and outside by the environment of the mould. The design variable is taken to be the shape of the inner surface of the plunger cavity.

The cost functional is the second power of the norm in the weighted space L r 2 of difference of trace of temperature from given constant, which is evaluated on the outward boundary of the plunger.

Existence and uniqueness of the state problem solution and existence of a solution of the optimization problem are proved.

Keywords

shape optimization heat-conducting fluid energy transfer 

MSC 2010

49Q10 76D55 93C20 

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References

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    J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design: Theory and Applications. John Wiley & Sons, Chichester, 1988.zbMATHGoogle Scholar
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    A. Kufner: Weighted Sobolev Spaces. Licensed ed. A Wiley-Interscience Publication. John Wiley & Sons, Chichester, 1985.Google Scholar
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    K. Rektorys: Variational Methods in Mathematics, Science and Engineering. Translated from the Czech by Michael Basch. D. Reidel Publishing Company, Dordrecht, 1975.zbMATHGoogle Scholar
  4. [4]
    S. N. Šorin: Sharing Heat. SNTL-Publishers of Technical Literature, Praha, 1968.Google Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2013

Authors and Affiliations

  1. 1.Technical University of LiberecLiberec 1Czech Republic

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