Computational Physics in the Advanced Lab: Experiment and Simulation of Thermal Diffusion in Metal Rods

We present a simple experiment on thermal diffusion in metal rods that can be used to integrate computation into the advanced lab. An analytical solution exists for the transient heat conduction in an infinite rod with a delta function heat input, but no analytical solution exists for short rods or for long duration heat inputs. Our apparatus is a copper rod with a heater and thermometers attached to the rod. The temperature of the metal rod due to transient heat conduction can be modeled using a simple numerical simulation and the finite centered difference method. Using a 22 cm long copper rod with the ends thermally sunk in aluminum blocks, we show poor agreement between the experimental results and the infinite-rod analytical model, but excellent agreement between the experimental results and our numerical simulation. This experiment shows the power of a numerical simulation but also the limitations of the chosen model, which can be used as motivation for further exploration.