Abstract

Citation

Researchers should cite this work as follows:

• Spayd, K., Puckett, J. (2022). 9-020-HeatDiffusion-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/WFSN-Q683

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Article Context

Description

This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario in which heat energy diffuses through a long, thin metal rod that has one of its ends submerged in hot water and the other end in room-temperature water. Students then investigate the subtleties of analytical and numerical techniques used to solve the initial boundary value problem. Finally, the experimental data can be used to compare the theoretical model with the physical phenomenon.

The physical phenomenon of heat diffusion in a long thin metal rod is measurable with the experimental design illustrated. The ends of the rod are submerged in water baths at different temperatures and the heat from the hot water bath travels through the metal to the cooler end. The temperature of the rod is measured at four locations; those measurements are sent to a Raspberry Pi, which processes the raw data and sends the collated data to be displayed on the computer screen.

If you are not collecting your own data, a data set from the authors is provided in an Excel spreadsheet in which you can find the time and temperature data shown.