M. M. Chen

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.

Effect of surface tension gradient driven convection in a laser melt pool: Three‐dimensional perturbation model

A three‐dimensional model of the thermocapillary flow within the molten region during laser surface heating is developed. This physically corresponds to the process of a stationary laser beam irradiating on the surface of a moving workpiece. The recirculating flow due to the surface tension gradient is much faster than the scanning motion. This allows a perturbation solution. The basic solution corresponds to the stationary axisymmetric case, and the perturbation is based on a small scanning velocity. The advantage of seeking a perturbation solution is that the three‐dimensional flow is modeled by two sets of two‐dimensional equations which are presumably much more tractable than the original three‐dimensional equations. Numerical solutions are obtained. The solid‐liquid interface is determined by an iterative scheme. In the presence of the recirculating flow, the heat transfer becomes convection dominated. The absorbed laser energy is convected sideways so that a wider and shallower molten region is obta...

Asymptotic Solution for Thermocapillary Flow at High and Low Prandtl Numbers Due to Concentrated Surface Heating

Thermocapillary convection due to nonuniform surface heating is the dominant form of fluid motion in many materials processing operations. The velocity and temperature distributions for the region adjacent to the area of peak surface heating are analyzed for the limiting cases of large and small Prandtl numbers. For a melt pool whose depth and width are large and small Prandtl numbers. For a melt pool whose depth and width are large relative to the thermal and viscous boundary layers, it is shown that the most important parameter is the curvature (i.e., {gradient}{sup 2}q) of the surface heat flux distribution. The solutions of the temperature and stream functions are presented, some of which are in closed form. Simple, explicit expressions for the velocity and maximum temperature are presented. These results are found to be quite accurate for realistic Prandtl number ranges, in comparison with exact solutions for finite Prandtl numbers. Besides being more concise than exact results, the asymptotic results also display the Prandtl number dependence more clearly in the respective ranges.

THREE-DIMENSIONAL MODEL FOR CONVECTION IN LASER MELTED POOL.

A three-dimensional axis-symmetry model of the fluid flow and heat transfer of laser melted pool is developed. The model corresponds physically to a stationary laser source. Non-dimensional form of the governing equations are derived. Four dimensionless parameters arise from the non-dimensionalization, namely, Marangoni number (Ma), Prandtl number (Pr), Dimensionless melting temperature (Tm*), and Radiation factor (RF). Their effects and significances are discussed. Numerical solutions are obtained. The solid liquid interface, which is not known a priori, is solved. Quantitative effects of the dimensionless parameters on pool shape are obtained. In the presence of the flow field, the heat transfer becomes convection dominated. Its effect on isotherms within the molten pool is discussed. Experimental results are also obtained and presented.A three-dimensional axis-symmetry model of the fluid flow and heat transfer of laser melted pool is developed. The model corresponds physically to a stationary laser source. Non-dimensional form of the governing equations are derived. Four dimensionless parameters arise from the non-dimensionalization, namely, Marangoni number (Ma), Prandtl number (Pr), Dimensionless melting temperature (Tm*), and Radiation factor (RF). Their effects and significances are discussed. Numerical solutions are obtained. The solid liquid interface, which is not known a priori, is solved. Quantitative effects of the dimensionless parameters on pool shape are obtained. In the presence of the flow field, the heat transfer becomes convection dominated. Its effect on isotherms within the molten pool is discussed. Experimental results are also obtained and presented.