MARANGONI CONVECTION WITH TWO FREE SURFACES

REFERENCES

• C. Cuvelier and J. M. Driessen , Thermocapillary Free Boundaries in Crystal Growth , J. Fluid Mech. , vol. 169 , pp. 1 – 26 , 1986 .
   Web of Science ®Google Scholar
• J.-C. Chen and F.-S. Hwu , Oscillatory Thermocapillary Flow in a Rectangular Cavity , Int. J. Heat Mass Transfer , vol. 36 , pp. 3743 – 3749 , 1993 .
   Web of Science ®Google Scholar
• A. K. Sen , Thermocapillary Convection in a Rectangular Cavity with a Deformable Interface , Phys. Fluids , vol. 29 , pp. 3881 – 3883 , 1986 .
   Web of Science ®Google Scholar
• M. E. Thompson and J. Szekely , The Transient Behavior of Weld Pools with a Deformed Free Surface , Int. J. Heat Mass Transfer , vol. 32 , pp. 1007 – 1019 , 1989 .
   Web of Science ®Google Scholar
• R. T. C. Choo , J. Szekely , and R. C. Westhoff , Modeling of High-Current Arcs with Emphasis on Free Surface Phenomena in the Weld Pool , Welding J. , vol. 69 , pp. 346s – 361s , 1990 .
   Web of Science ®Google Scholar
• M. C. Tsai and S. Kou , Marangoni Convection in Weld Pools with a Free Surface , Int. J. Numer. Methods Fluids , vol. 9 , pp. 1503 – 1516 , 1989 .
   Web of Science ®Google Scholar
• S. D. Kim and S. J. Na , Effect of Weld Pool Deformation on Weld Penetration in Stationary Gas Tungsten Arc Welding , Welding J. , vol. 71 , pp. 179s – 193s , 1992 .
   Web of Science ®Google Scholar
• Y. H. Xiao and G. D. Ouden , A Study of GTA Weld Pool Oscillation , Welding J. , vol. 69 , pp. 289s – 293s , 1990 .
   Web of Science ®Google Scholar
• Y. H. Xiao and G. D. Ouden , Weld Pool Oscillation during GTA Welding of Mild Steel , Welding J. , vol. 72 , pp. 428s – 434s , 1993 .
   Web of Science ®Google Scholar
• C. D. Sorenson and T. W. Eagar , Modeling of Oscillations in Partially Penetrated Weld Pools , J. Dynam. Systems Measur. Control , vol. 112 , pp. 469 – 474 , 1990 .
   Web of Science ®Google Scholar
• Y. Chen , Thermocapillary Flows with Free Surfaces, Center for Computational Sciences , University of Kentucky , 1994 .
   Google Scholar
• P. M. Gresho , On the Theory of Semi-Implicit Projection Methods for Viscous Incompressible Flow and its Implementation via a Finite Element Method that Also Introduces a Nearly Consistent Mass Matrix. Part 1 Theory , Int. J. Numer. Methods Fluids , vol. 11 , pp. 587 – 620 , 1990 .
   Web of Science ®Google Scholar
• A. K. Sen and S. H. Davis , Steady Thermocapillary Flows in Two-Dimensional Slot , J. Fluid Mech. , vol. 121 , pp. 163 – 186 , 1982 .
   Web of Science ®Google Scholar
• D. Rivas , High-Reynolds-Number Thermocapillary Flows in Shallow Enclosures , Phys. Fluids , vol. 3A ( 2 ), pp. 280 – 291 , 1990 .
   Google Scholar
• Address correspondence to T. Zacharia, Oak Ridge National Laboratory, P.O. Box 2008, MS 6140, Oak Ridge, TN 37831.
   Google Scholar