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shape optimization; Navier-Stokes equations; heat transfer
This contribution presents the shape optimization problem of the plunger cooling cavity for the time dependent model of pressing the glass products. The system of the mould, the glass piece, the plunger and the plunger cavity is considered in four consecutive time intervals during which the plunger moves between 6 glass moulds. \endgraf The state problem is represented by the steady-state Navier-Stokes equations in the cavity and the doubly periodic energy equation in the whole system, under the assumption of rotational symmetry, supplemented by suitable boundary conditions. \endgraf The cost functional is defined as the squared weighted $ L^2 $ norm of the difference between a prescribed constant and the temperature of the plunger surface layer at the moment before separation of the plunger and the glass piece. \endgraf The existence and uniqueness of the solution to the state problem and the existence of a solution to the optimization problem are proved.
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