Laser heating and melting of thin films with time-dependent absorptance. II: An exact solution for time intervals greater than the transit time

Laser heating and melting are studied considering the laser-induced reflectivity variations R(τ). The study is made for time intervals greater than the transit time τs using the Fourier series expansion technique together with the differential and integral forms of the heat diffusion equation. The obtained results reveal that the equations for the thickness Z(τ) of the molten layer and the rate of melting Z′(τ) are no longer quadratic. A fourth-degree algebraic equation for Z(τ) is obtained similar to that derived for the previous stage τ≤τs, but with different coefficients. Moreover, it is shown that the obtained rate of melting for the considered stage is no longer a constant one. Computations on a thin silver film as an illustrative example for the considered stage are carried out.