Closed-form solution of Cattaneo equation including volumetric source in relation to laser short-pulse heating

Abstract

The wave nature of the heating model is considered, incorporating the Cattaneo equation with the presence of a volumetric heat source. The volumetric heat generation resembles the step input laser short-pulse intensity. The governing of the heat equation is solved analytically using the Laplace transformation method. The stress field generated due to thermal contraction and expansion of the substrate material is formulated and the closed-form solution is presented. It is found that the wave nature of the heating is dominant during the period of the irradiated short-pulse; however, in the late cooling period, the wave nature of heating is replaced by diffusional heat conduction, governed by Fourier’s law. The stress field during the heating cycle is compressive and becomes tensile in the cooling cycle.