Optimal design of the cooling plunger cavity

Petr Salač

Applications of Mathematics (2013)

  • Volume: 58, Issue: 4, page 405-422
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Salač, Petr. "Optimal design of the cooling plunger cavity." Applications of Mathematics 58.4 (2013): 405-422. <http://eudml.org/doc/260664>.

@article{Salač2013,
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 $L^2_r$ 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.},
author = {Salač, Petr},
journal = {Applications of Mathematics},
keywords = {shape optimization; heat-conducting fluid; energy transfer; shape optimization; heat-conducting fluid; energy transfer},
language = {eng},
number = {4},
pages = {405-422},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Optimal design of the cooling plunger cavity},
url = {http://eudml.org/doc/260664},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Salač, Petr
TI - Optimal design of the cooling plunger cavity
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 405
EP - 422
AB - 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 $L^2_r$ 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.
LA - eng
KW - shape optimization; heat-conducting fluid; energy transfer; shape optimization; heat-conducting fluid; energy transfer
UR - http://eudml.org/doc/260664
ER -

References

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  1. Haslinger, J., Neittaanmäki, P., Finite Element Approximation for Optimal Shape Design: Theory and Applications, John Wiley & Sons Chichester (1988). (1988) Zbl0713.73062MR0982710
  2. Kufner, A., Weighted Sobolev Spaces. Licensed ed. A Wiley-Interscience Publication, John Wiley & Sons Chichester (1985). (1985) MR0802206
  3. Rektorys, K., Variational Methods in Mathematics, Science and Engineering. Translated from the Czech by Michael Basch, D. Reidel Publishing Company Dordrecht (1975). (1975) Zbl0371.35002MR0596582
  4. Šorin, S. N., Sharing Heat, SNTL-Publishers of Technical Literature Praha (1968). (1968) 

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