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Hyperbolic Nature of Heat Conduction for Short Pulse Laser Irradiation of Solid Surfaces: Analytical Solution for the Thermal Stress Field
H.R. Al-Duhaim, B.S. Yilbasbas and F.D. Zaman

Temperature and thermal stress fields are formulated analytically for a laser short-pulse heating of a solid material. The step input pulse intensity is considered to resemble the laser heating situation. In the analysis, the Laplace transform in time and the Fourier cosine transform in space are incorporated to solve the hyperbolic heat conduction equation with the appropriate initial and boundary conditions. Thermal stress field is also obtained through coupling heat and thermal stress equations with the heat equation. The integral transforms are used to obtain the solutions of the coupled equations. The inversion of the Laplace transform is performed using second shifting theorem of Laplace transform while Mathematica is used for the inverse Fourier cosine transform. It is found that temperature rise in the irradiated region is rapid during the heating pulse because of the volumetric heat source incorporated in the analysis. Temperature decay is also rapid in the early cooling periods; however, as the cooling period progresses, temperature decay becomes gradual. Thermal stress is compressive and it shows a wave behaviour within the substrate material.

Keywords: Laser, short pulse, heating, analytical solution, thermal stress, hyperbolic heat conduction equation, Laplace transformation, Fourier cosine transformation

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