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

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. PACS No: 44.10.+i Nous etudions la nature ondulatoire du modele de chauffage incorporant l'equation de Cattaneo, avec la presence de la source volumique de chaleur. La generation volumique de chaleur ressemble a intensite d'un laser a impulsion courte avec signal d'entree en echelon. Nous solutionnons analytiquement l'equation gouvernante de la chaleur en utilisant la methode de la transformation de Laplace. Le champ de contrainte genere par la contraction et l'expansion thermique du materiel du substrat est mis en formule et nous en presentons une solution analytique. Nous trouvons que le caractere ondulatoire du chauffage est dominant pendant la periode d' irradiation en impulsion courte, mais la conduction de chaleur de Fourier par diffusion domine la periode du refroidissement. Le champ de contrainte est en compression pendant le chauffage, mais en etirement pendant le refroidissement. [Traduit par la Redaction]
1. Introduction In short-pulse laser heating of metal surfaces, the absorption depth is small and the heating time is short. This results in a heat wave propagatiing at finite speed [...]