Applications of Mathematics

, Volume 63, Issue 6, pp 643–664 | Cite as

Numerical solution of the pressing devices shape optimization problem in the glass industry

  • Petr SalačEmail author


In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered. The state problem is given as a multiphysics problem where solidifying molten glass is cooled from the inside by water flowing through the plunger cavity and from the outside by the environment surrounding the mould.

The cost functional is defined as the squared \(L^2_r\) norm of the difference between a prescribed constant and the temperature on the outward boundary of the plunger. The temperature distribution is controlled by changing the insulation barrier wall thickness.

The numerical results of the optimization to the required target temperature 800 ◦C of the outward plunger surface together with the distribution of temperatures along the interface between the plunger and the glass piece before, during and after the optimization process are presented.


shape optimization heat-conducting fluid energy transfer 

MSC 2010

49Q10 76D55 93C20 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Haslinger, P. Neittaanmäki: Finite Element Approximation for Optimal Shape Design: Theory and Applications. John Wiley & Sons, Chichester, 1988.zbMATHGoogle Scholar
  2. [2]
    A. Kufner: Weighted Sobolev Spaces. A Wiley–Interscience Publication, John Wiley & Sons, New York, 1985.Google Scholar
  3. [3]
    I. Matoušek, J. Cibulka: Analýza tvarovacího cyklu na karuselovém lisu NOVA. TU v Liberci, Liberec, 1999. (In Czech.)Google Scholar
  4. [4]
    P. Salač: Optimal design of the cooling plunger cavity. Appl. Math., Praha 58 (2013), 405–422.MathSciNetCrossRefGoogle Scholar
  5. [5]
    P. Salač: Optimization of plunger cavity. Programs and Algorithms of Numerical Mathematics 16, 2012 (J. Chleboun et al., eds.). Academy of Sciences of the Czech Republic, Institute of Mathematics, Praha, 2013, pp. 174–180.zbMATHGoogle Scholar
  6. [6]
    P. Salač, M. Starý: The cooling of the pressing device in the glass industry. Internat. J. Multiphysics 7 (2013), 207–218.CrossRefGoogle Scholar
  7. [7]
    S. N. Šorin: Sdílení Tepla. SNTL, Praha, 1968. (In Czech.)Google Scholar

Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Technical University of LiberecLiberec 1Czech Republic

Personalised recommendations