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Keywords:
shape optimization; heat-conducting fluid; energy transfer
shape optimization; heat-conducting fluid; energy transfer
Summary:
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.
References:
[1] Haslinger, J., Neittaanmäki, P.: Finite Element Approximation for Optimal Shape Design: Theory and Applications. John Wiley & Sons Chichester (1988). MR 0982710 | Zbl 0713.73062
[2] Kufner, A.: Weighted Sobolev Spaces. Licensed ed. A Wiley-Interscience Publication. John Wiley & Sons Chichester (1985). MR 0802206
[3] Rektorys, K.: Variational Methods in Mathematics, Science and Engineering. Translated from the Czech by Michael Basch. D. Reidel Publishing Company Dordrecht (1975). MR 0596582 | Zbl 0371.35002
[4] Šorin, S. N.: Sharing Heat. SNTL-Publishers of Technical Literature Praha (1968).
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