Analytical solution for pulsed laser heating process: Convective boundary condition case

Laser pulse heating offers considerable advantages over the conventional heating methods in industry. In laser industrial applications, in general, an assisting gas is used, which results in convective cooling of the surface during the heating process. Moreover, modelling of the heating process reduces the experimental cost and enhances the understanding of the physical processes involved. In the present study, laser pulse heating of metallic substrates with convective boundary condition at the surface is considered. The time exponentially varying laser pulse is employed in the analysis. A closed form solution pertinent to laser time exponentially varying pulse is obtained using a Laplace transformation method. It is found that analytical solution becomes identical to that obtained previously for a step input pulse intensity when the pulse parameters (β and γ) are set to zero. The effect of Biot number (Bi) on the temperature profiles becomes significant as Bi ≥ 0.202. Moreover, pulse parameter (β/γ) has considerable influence on the temperature profiles, in which case, temperature attains low values as β/γ becomes high.