A closed form solution for temperature rise inside solid substrate due to time exponentially varying pulse

Modeling of laser heating process minimizes the experimental cost and enables to optimize the process parameters for improved end product quality. In the present study, an analytical solution for laser conduction limited heating due to time exponentially varying pulse is presented. The governing equation of heat diffusion is solved analytically using a Laplace transformation method. The closed form solution is validated by a solution for a step input pulse intensity presented in the previous study as well as numerical predictions. Temperature rise inside the substrate material is computed for steel. It is found that the present solution reduces to previous solution once the pulse parameter (β = 0) are set to zero. Temperatures obtained from the closed form solution agree well with the numerical predictions. Moreover, temperature rises rapidly in the surface vicinity due to time exponentially varying pulse. The pulse parameter (β* / γ*) has a significant effect on the temperature rise. In this case, low value of (β* / γ*) results in high temperature rise in the surface vicinity of the substrate material.