A two-dimensional transient model for convection in laser melted pool

A two-dimensional transient model for convective heat transfer and surface tension driven fluid flow is developed. The model describes the transient behavior of the heat transfer process of a stationary band source. Semi-quantitative understanding of scanning is obtained by a coordinate transformation. The non-dimensional forms of the equations are derived and four dimensionless parameters are identified, namely, Peclet number (Pe), Prandtl number (Pr), surface tension number(S), and dimensionless melting temperature(@#@ Tm * @#@). Their governing characteristics and their effects on pool shape, cooling rate, velocity field, and solute redistribution are discussed. A numerical solution is obtained and presented. Quantitative effects of Prandtl number and surface tension number on surface velocity, surface temperature, pool shape, and cooling rate are presented graphically.