A Simple Method to Determine Temperature Dependency of Thermal Diffusivity

We used the method we proposed previously (American Journal of Physics 90, 568 (2022); https://doi.org/10.1119/5.0087135) to further study thermal diffusivity's temperature dependency. Spheres of different radii, 15 mm, 20 mm, and 25mm, made of PMMA (Poly(methyl methacrylate)), are used to demonstrate the effectiveness of this method. We drilled a narrow channel to the center of the spherical shapes, inserted a thermocouple sensor into the center, and immersed the ball in boiling water. The center temperature was measured as a function of time. We tried to fit the time dependence of the center temperature to a heat-conduction model, with thermal diffusivity as a fitting parameter. We found that thermal diffusivity needs to be temperature dependent in order to obtain a good and consistent fitting result for all the samples. We developed a theoretical model which takes temperature dependency of thermal diffusivity into consideration. The derived thermal diffusivity and its temperature dependency for PMMA have good agreement with the data published in prior research.