Temperature field of a moving point source with change of state

Abstract A theoretical simulation of automatic welding as a moving point source of heat with conduction as the dominant mode of transfer is refined to incorporate change of state across the melt boundary. Matched asymptotic expansions are used to solve the singular perturbation problem associated with arbitrary latent heat, and small values of source dimensionless velocity—power product. The problem is mathematically analogous to scattering of long waves off a sphere. It is shown that previous empirical estimates which subtract the latent heat power from the corresponding input quantity seriously over-predict the effect of change of state on weld depth.