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.

Infrared imaging of a non-stationary thermal conductive process and observation of its Green’s kernel / Oss, Stefano. - In: EUROPEAN JOURNAL OF PHYSICS. - ISSN 0143-0807. - 41:1(2019), pp. 01510201-01510220. [10.1088/1361-6404/ab4680]

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

Oss, Stefano
2019

Abstract

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.
1
Oss, Stefano
Infrared imaging of a non-stationary thermal conductive process and observation of its Green’s kernel / Oss, Stefano. - In: EUROPEAN JOURNAL OF PHYSICS. - ISSN 0143-0807. - 41:1(2019), pp. 01510201-01510220. [10.1088/1361-6404/ab4680]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/246298
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