Spatial and temporal temperature evolution of rotating tubes heated by a Gaussian laser beam – analytical solutions and calculations

Abstract

PurposeThis paper aims to give an extended analytical solution for the thermal evolution of rotating tubes irradiated by a Gaussian laser beam. The heating process of opaque targets by surface absorption of laser radiation is a topic of fundamental importance in many civilian and military applications (e.g. hollow tube processing, counter of rockets, mortars and artillery shells). The spatio-temporal distribution of the temperature is analytically determined by the heat equation. Explicit solutions of this parabolic partial differential equation only exist for specific cases such as flat surfaces and specific beam profiles.Design/methodology/approachIn this paper, the author derives an explicit function that allows the calculation of the spatio-temporal temperature for the case of a tube irradiated by a laser beam. For this purpose, the tube geometry is transformed on that of an infinite extended slab. The heat source is transformed by the method of images to be periodically placed on the slab. Furthermore, the derived formula concerns even a rotation of the tube around the longitudinal axis.FindingsFrom the calculations, the strong decrease in maximum temperatures and the spatio-temporal modulation could quantitatively be shown. For high rotation speeds, the modulation shows a falling tendency and the temperature approaches an asymptotic evolution. For this spatio-temporal evolution, the author found also an analytical expression allowing a relatively easy and fast calculation formula.Originality/valueThe analytical solutions were used for further calculations concerning the thermal ignition of encased explosives in rotating tubes. With the help of the formulas, the ignition times over a broad parameter range were determined.