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Research Papers: Heat Transfer in Manufacturing

Scaling Weld or Melt Pool Shape Affected by Thermocapillary Convection With High Prandtl Numbers

[+] Author and Article Information
P. S. Wei, C. L. Lin, H. J. Liu, T. DebRoy

Department of Mechanical and Electro-Mechanical Engineering,  National Sun Yat-Sen University, Kaohsiung, Taiwan, R.O.C.pswei@mail.nsysu.edu.twDepartment of Materials Science and Engineering,  The Pennsylvania State University, University Park, PA 16802, e-mail: rtd1@psu.edupswei@mail.nsysu.edu.tw

J. Heat Transfer 134(4), 042101 (Feb 16, 2012) (10 pages) doi:10.1115/1.4005206 History: Received March 23, 2011; Revised September 22, 2011; Published February 16, 2012; Online February 16, 2012

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.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Schematic sketch of surface velocity and temperature, and distinct regions for analysis

Grahic Jump Location
Figure 2

Scaling based on (a) energy balance in solid surrounding molten pool, (b) momentum balance in the hot region, (c) energy balance in the hot region, (d) momentum balance in the cold corner region, (e) conservation of energy in the intermediate region between the hot and cold corner region, and (f) total energy balance from incident energy to energy dissipated into solid

Grahic Jump Location
Figure 3

Scaled transport variables for Prandtl numbers 1 ≤ Pr < 4 for (a) molten pool depth, (b) molten pool width, (c) peak surface velocity, (d) peak surface temperature, (e) secondary peak surface velocity, and (f) maximum temperature in the cold corner region, which are uncoupled and functions of working variables

Grahic Jump Location
Figure 4

Scaled transport variables for Prandtl numbers Pr ≥ 4 for (a) molten pool depth, (b) molten pool width, (c) peak surface velocity, (d) peak surface temperature, (e) secondary peak surface velocity, and (f) maximum temperature in the cold corner region, which are uncoupled and functions of working variables

Grahic Jump Location
Figure 5

Continuity of molten pool depth between Prandtl numbers of 3 and 4

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