# Institute of Mathematics

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

#### Petr Salač

###### Received September 19, 2017.   Published online November 16, 2018.

Abstract:  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 \${}^{\circ} \$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.
Keywords:  shape optimization; heat-conducting fluid; energy transfer
Classification MSC:  49Q10, 76D55, 93C20
DOI:  10.21136/AM.2018.0247-17

References:
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[4] P. Salač: Optimal design of the cooling plunger cavity. Appl. Math., Praha 58 (2013), 405-422. DOI 10.1007/s10492-013-0020-8 | MR 3083521 | Zbl 1289.49043
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Affiliations:   Petr Salač, Technical University of Liberec, Studentská 2, 461 17 Liberec 1, Czech Republic, e-mail: petr.salac@tul.cz

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