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A thermal analysis for laser heating and melting materials is derived for a Gaussian source moving at a constant velocity. The resulting temperature distribution, cooling rate distribution, and depth of melting are related to the laser spot size, velocity, and power level. As the power is increased to heat the liquid above the boiling point, a transition to deep penetration welding is described. Calculations are presented for 304-stainless steel which are in agreement with experiment.
Cline et al. (Thu,) studied this question.