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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design: Theory and Applications. John Wiley & Sons, Chichester, 1988.
A. Kufner: Weighted Sobolev Spaces. Licensed ed. A Wiley-Interscience Publication. John Wiley & Sons, Chichester, 1985.
K. Rektorys: Variational Methods in Mathematics, Science and Engineering. Translated from the Czech by Michael Basch. D. Reidel Publishing Company, Dordrecht, 1975.
S. N. Šorin: Sharing Heat. SNTL-Publishers of Technical Literature, Praha, 1968.
Author information
Authors and Affiliations
Corresponding author
Additional information
This work was supported by the Research plan No. MSM 4674788501 funded by Ministry of Education, Youth and Sports of the Czech Republic.
Rights and permissions
About this article
Cite this article
Salač, P. Optimal design of the cooling plunger cavity. Appl Math 58, 405–422 (2013). https://doi.org/10.1007/s10492-013-0020-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10492-013-0020-8