Closed form solution for temperature rise in a two layer assembly during laser step input pulse heating with the presence of convection cooling at surface

Laser step input pulse heating of a two layer assembly is considered and the closed form solution for temperature distribution in the assembly is presented. The volumetric heat source is incorporated in the analysis to account for the absorption of the irradiated filed. Laplace transformation method is introduced to solve the governing equation of heat conduction. The practical example for temperature formulation is presented for a two layer assembly consisting of steel and nickel. The convection cooling is incorporated in the analysis at the top surface of steel to account for the assisting gas effect during laser heating process. It is found that rate of temperature rise is high in the surface region during the early heating periods because of the internal energy gain from the irradiated field and low rate of heat diffusion from the irradiated region to its neighbourhood. The influence of convection cooling on temperature rise is considerable in the surface region, which is more pronounced at high Biot numbers. Temperature decay inside steel is gradual; however, it becomes sharp in nickel because of the differences in thermal conductivity of nickel and steel.