In this study, the peak surface velocity driven by thermocapillary force in melting or welding pool irradiated by a distributed low-power-density beam is determined from a scale analysis. In view of different distances of diffusion between momentum and energy, the effects of Prandtl number on surface velocity are of interest. A low-power-density-beam heating implies no deep and narrow cavity (or keyhole) taking place in the pool. The results find that the peak surface velocity is proportional to the first power and 2/3 power of the surface tension coefficient or Marangoni number for high and low Prandtl number, respectively. The free surface velocity is determined by Prandtl and Marangoni numbers for given dimensionless beam power and Peclet numbers. The predictions agree with numerical computations.

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