Heat conduction in a moving semi-infinite medium subject to laser irradiation is considered. The body of knowledge of exact analytical solutions for Gaussian laser irradiation is expanded to include pulsed lasers, and laser beams that penetrate into the medium with exponential decay. For applications with complicated geometries (laser melting and evaporation), a simple integral method, based on one-dimensional diffusion, is presented, and its range of validity determined.

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