optimal shape design; heat transfer; cooling; objective functional; rotational symmetry
In the contribution we present a problem of shape optimization of the cooling cavity of a plunger that is used in the forming process in the glass in dustry. A rotationally symmetric system of the mould, the glass piece, the plunger and the plunger cavity is considered. The state problem is given as a stationary heat conduction process. The system includes a heat source representing the glass piece that is cooled from inside by water flowing through the plunger cavity and from outside by the environment
surrounding the mould. The design variable is the shape of the inner surface of the plunger cavity. 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.