Optimization of the plunger cooling by the core with high thermal conductivity

The contribution deals with formulation of the optimization problem for the plunger which is cooled by the metal core with high thermal conductivity in combination with the insulation barrier with low thermal conductivity. The thermal energy is removed from the core to the water cooler and converted into steam there. Shape optimization of the core and the insulation barrier is carried out with the aim of achieving the prescribed constant temperature on the outer surface of the plunger at the time of separation of the plunger and the glass piece. The cost functional is the squared L-r(2) norm of the difference between the prescribed constant and the temperature on the outward boundary of the plunger at time of separation. The existence and uniqueness of the solution to the state problem and the existence of a solution to the shape optimization problem are introduced