Thermal Engineering: Optimization of an Industrial Furnace

Abstract

In this chapter we deal with a simple but realistic optimization problem. We have to find the optimal temperature of an industrial furnace in which are made resin pieces, such as car bumpers. The heating system is based on electric resistances, and the first part of this study is to compute the temperature field inside the oven when the values of the resistances are known. This work is called the direct problem: the resistances’ values are known and the temperature field is unknown. It is important here to emphasize that the mechanical properties of the bumper depend on the temperature during the cooking; so the second part of the study is devoted to computing the resistances’ values in order to maintain the bumper temperature at the “good” value. This optimization problem is called an inverse problem: the temperature is an input and the resistances values are outputs.