Three-dimensional axisymmetric model for convection in laser-melted pools

A three-dimensional axisymmetric model of the fluid flow and heat transfer in a laser-melted pool is developed. The model corresponds to the limiting case when the scanning velocity is small compared with the recirculating velocity. This model is also valid for spot welding. Non-dimensional forms of the governing equations are derived, from which four dimensionless parameters are obtained: the Marangoni number, the Prandtl number, the dimensionless melting temperature, and the radiation factor. Their effects and significance are discussed, and numerical solutions are obtained. The position and shape of the solid/liquid interface are obtained by an iterative scheme. The quantitative effects of the dimensionless parameters on pool shape are presented. In the presence of the flow field, the heat transfer becomes convection dominated. The effect of convection on isotherms within the molten pool is discussed, and experimental results are presented.