Thermal Engineering: Optimization of an Industrial Furnace

Ionut Danaila (), Pascal Joly, Sidi Mahmoud Kaber and Marie Postel
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Ionut Danaila: Université de Rouen Normandie, CNRS, Laboratoire de mathématiques Raphaël Salem
Pascal Joly: Laboratoire Jacques-Louis Lions
Sidi Mahmoud Kaber: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions
Marie Postel: Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions

Chapter Chapter 14 in An Introduction to Scientific Computing, 2023, pp 309-325 from Springer

Abstract: Abstract In this chapter, we deal with a simple but realistic optimization problem. We have to find the optimal temperature in an industrial furnace, used to form 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 step is called the direct problem: the resistances’ values are known and the temperature field is unknown. The second part of the study is devoted to computing the resistances’ values in order to maintain the bumper temperature at a prescribed value. This optimization problem is called an inverse problem: the temperature is the input and the resistances values are the outputs. For the numerical implementation, we use 2D triangular finite elements.

Date: 2023
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DOI: 10.1007/978-3-031-35032-0_14

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