A Closed Form Solution of Temperature and Stress Fields for Laser Short-Pulse Heating of a Solid: Exponentially Decaying Volumetric Source
A semi-infinite medium subjected to a short pulse heating is considered in this work. Cattaneo equation with a volumetric source changing with the depth of the solid is employed to model the problem. Analytical solutions for both temperature and thermal stresses are obtained using Laplace transformation approach. The wavelike behaviour of the heating is reflected in the formulation by using the hyperbolic Cattaneo equation. The temperature response is observed to be rapid in the early heating period and sluggish as the heating period advances. Stresses closer to the surface are compressive during the heating and they become tensile as cooling takes place.
Keywords: Cattaneo equation, analytical solution, laser, short pulse, heating, volumetric source, thermal stress