Abstract:

Mathematics is usually a hurdle students have to jump over in order to understand physics. Many of them get lost in the mathematical details and don’t get the basic physical facts.

Heat transfer analysis is very important in engineering studies due to its wide range of applications: energy use and conversion, materials fabrication …. It is common practice to introduce in the freshman year of these studies the analysis of this problem in the steady state, neglecting the transient state because of its mathematical complexity for first year students with no knowledge of differential equations. It is very hard to see this phenomenon in the laboratory, not only because of the time scale of the transient state but also because it is difficult to put enough temperature sensors inside a solid system to get a clear picture of the temperature distribution at a given time. Nevertheless, it would interesting for the students to have a glimpse of the way heat flows during the transient state in order to get an overall view of heat transfer processes.

We pretend with this work to help the professor in presenting this subject and the students in understanding the analysis of this phenomenon. We have developed a Mathematica® [1] notebook for studying the temperature field in the transient state for a finite-width wall. The notebook calculates the temperature of any point of the wall at any time and generates an animation that shows the way the temperature field changes with time. In this way, the students see how the steady state is reached without having to deal with complex equations.

Moreover the technique we have developed can be easily adapted to other physical problems related to similar differential equations (for instance transients in electric circuits). In this way, it would be possible for the students to grasp complex systems without having to bother with the underlying mathematics. They would get at the same time an enhanced learning experience and a deeper understanding of the phenomena governed by this kind of equations.

References:
[1] www.wolfram.com

Keywords:

Computer simulation, heat transfer, transient state, Mathematica.