This is an experiment on thermal diffusion in which combining experimentation and computational modeling is required to understand the data. The experiment is conceptually simple: a heat pulse from a resistive heater is applied to a portion of a thin copper rod, and thermistors measure the temperature at different locations along the rod as a function of time. The time evolution of the temperature in the rod is governed by the diffusion equation. An analytic solution is possible for a short-duration heat pulse delivered by a small heater to a very long rod. Yet, interpreting measurements with longer heat pulses, larger heaters, and shorter rods necessitates numerically solving the diffusion equation. This experiment is therefore an excellent opportunity for upper-division students to integrate experimental and computational physics and to build skills that are of increasing value in the workforce and in research.

The experimental setup consists of a copper rod supported by a 3D-printed plastic frame. The rod is threaded at both ends to optionally connect aluminum heat sinks to vary the boundary conditions at the rod ends. A resistive heater and four thermistors are attached to the rod. The entire apparatus may optionally be operated in vacuum to reduce non-radiative heat loss. (For more details, please see Refs. [1] and [2].)

 During the Immersion, participants will collect thermal diffusion data and then work through pedagogical materials that guide a student in developing a computational model for the experiment. The model will numerically solve the 1D diffusion equation using a finite-difference scheme. Ultimately, the goal is for participants to fit their own computational model to their own data. Time permitting, participants may also work on implementing more sophisticated numerical techniques, hardware interfacing, and/or building their own setup. (We anticipate having some flexibility to meet the participants’ experience and interests.)

 For computational modeling during the Immersion, we will use free and open-source Python tools. However, we can provide some support for other programming environments such as MATLAB. Participants should have some basic programming experience (preferably in Python), but introductory materials will be distributed to help participants with no programming experience develop basic skills before the Immersion. Furthermore, the portion of the Immersion focusing on computational modeling will be self-paced with mentor guidance. Participants should bring a laptop, although we can provide computers if necessary.

 The cost of implementing the experiment is approximately $200. A USB data acquisition interface is also required but may be purchased for approximately $700 if not already available. Other required electronic test and measurement equipment (power supplies, an oscilloscope) is available in most laboratories. If desired and not already available, an optional low-vacuum setup can be purchased for approximately $2500.

 [1] Y. Mohod and M. C. Sullivan, “Computational physics in the advanced lab: Experiment and simulation of thermal diffusion in metal rods,” American Journal of Physics 93, 730-736 (2025). https://doi.org/10.1119/5.0269525

 [2] M. C. Sullivan, B. G. Thompson, and A. P. Williamson, “An experiment on the dynamics of thermal diffusion,” American Journal of Physics 76, 637-642 (2008). https://doi.org/10.1119/1.2888544