Infrared imaging of a non-stationary thermal conductive process and observation of its Green's kernel

A simple experiment is devised to visualize, through the infrared thermal imaging technique, the time dependence of the transient temperature distribution in a solid, metallic rod. The Laplace transform method is adopted to obtain a theoretical model which is numerically solved. The particular case of a thermal shock imposed to one end of a single rod is then considered and a simplified form of the Laplace transform solution is analytically developed. The resulting expression is shown to constitute the Green's heat kernel for the rod problem. This propagator has a simple analytical expression which allows for its explicit study and comparison with the experimental temperatures. The onset of a 'heat wave' and its temperature peak is observed and described within the Green fundamental solution. Further comparisons are also made in terms of numerical simulations based on a free app devoted to thermal partial differential equations. The experiment and the mathematical treatment here presented have been developed especially for undergraduate physics students in an educational framework. © 2019 European Physical Society.