Laser melting of solids—An exact solution for time intervals less or equal to the transit time

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Abstract
The thickness of the molten layer and the rate of melting induced by constant laser irradiance in a solid slab is studied. The study is carried out for time intervals less than or equal to the transit time, defined as the time taken for the temperature of the rear surface to change from ambient. The integral form of the heat conduction equation with the boundary condition at the interfacial surface between the liquid and solid phases together with a suggested model for the melting process is used to obtain an exact solution for the considered problem. Computations for a slab of aluminum of thickness 3×10−4 m subjected to laser irradiance of value q0=1014 W/m2 are carried out. It is found that the rate of melting after a certain delay time attains a constant value.