Scaling weld or melt pool shape affected by thermocapillary convection with high prandtl numbers

The molten pool shape and thermocapillary convection during melting or welding of metals or alloys are self-consistently predicted from scale analysis. Determination of the molten pool shape and transport variables is crucial due to their close relationship with the strength and properties of the fusion zone. In this work, surface tension coefficient is considered to be negative, indicating an outward surface flow, whereas high Prandtl number represents a reduced thickness of the thermal boundary layer compared to that of the momentum boundary layer. Since the Marangoni number is usually very high, the domain of scaling is divided into hot, intermediate and cold corner regions, boundary layers along the solid-liquid interface and ahead of the melting front. The results show that the width and depth of the pool, peak and secondary surface velocities, and maximum temperatures in the hot and cold corner regions can be explicitly and separately determined as functions of working variables, or Marangoni, Prandtl, Peclet, Stefan, and beam power numbers. The scaled results agree with numerical results and available experimental data.