Cooling process of metal

Large metal structures, such as steel posts used in bridge constructions, are cast in molds and then cooled so that they can be installed. When metals cool, they change their structure. Their state of aggregation changes from liquid to solid. This is called crystallization. In the process, the so-called heat of crystallization is released, which slows down and even reverses the cooling process. If the cooling process is not known precisely enough, this can lead to damaged products during casting, making them less stable.

For the company RWP GmbH (Richter, Weiß and Partners, named after the founders of the company Wieland Richter and Konrad Weiß), it is therefore important for the casting of metals to

  • know the temperature and the time of crystallization and
  • to determine the amount of energy released.

Integration and differentiation are needed to solve these two subproblems. The material gives students real-world applications of high school mathematics, which contributes to their motivation.

Duration: 2 double lessons
Contents: Differentiation, difference quotient, integration, sum of squares, measurement error.
Prior knowledge: Differentiation, difference quotient, integration, sum of squares.
Applicable: For upper level students
Created by: Kirsten Wohak
Registration: Dates can be arranged individually by e-mail at KIT or at RWTH.

 

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