Laser Step Input Pulse Heating of a Finite Thickness Solid: Closed Form Solution of Temperature Rise
Laser pulse heating of a finite thickness solid is considered and temperature field is formulated for the laser step input pulse irradiation. The Laplace transformation method is used to solve the governing heat equation with relevant boundary and initial conditions. The Dawson’s integral method is adapted to inverse the Laplace solution to the physical plane. Temporal variation of temperature in the irradiated region is computed for various laser pulse lengths by using the closed form solution of temperature field derived in this study. It is found that temperature rise in the early heating period is rapid because of the internal energy gain from the irradiated laser field and attainment of low temperature gradient in this region during the early heating period. Temperature decay is fast at the surface in the early cooling period, which is particularly true for laser long pulses. Temperature decays sharply in the region next to the surface vicinity, which is more pronounced for long laser pulses. Increased temperature gradient enhances heat diffusion from the surface region towards the solid bulk. In the case of laser short pulse lengths, temperature decay below the surface remains gradual because of the attainment of the low temperature gradients below the surface.
Keywords: Laser heating, finite thickness solid, temperature, step input pulses, analytical solution, mathematical model, laplace, dawson’s integral method