Determination of Temperature Distribution and Thermal Stress for the Hyperbolic Heat Conduction Equation Due to Laser Short Pulse Heating
H.R. Al-Duhaim, B.S. Yilbas and F.D. Zaman
We consider the hyperbolic heat conduction model and obtain the analytical solution for the laser short pulse heating of a solid surface. In order to account for the absorption of the incident laser energy, a volumetric source is incorporated in the analysis. The Laplace transform in time and the Fourier cosine transform in space variable are employed to find solution of the problem in the transformation domain. The inversion of the solution from the transform plane is carried out using an analytical approach. We also consider thermal stress development in the irradiated region due to the presence of the volumetric heat source. It is found that temperature rise at the surface follows almost the laser pulse behaviour and decay of temperature is sharp in the region next to the surface vicinity of the substrate material. Thermal stress is compressive in the surface region and shows wave behaviour with progressing time.
Keywords: Laser pulse, temperature, thermal stress, hyperbolic heat conduction equation, analytical solution, laser heating, short pulse