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1 1 Tsai, M.C. and Kou, S. (1990). Heat transfer and fluid flow in welding arcs produced by sharpened and flat electrodes. International Journal of Heat and Mass Transfer 33 (10): 2089–2098.

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3 3 Ushio, M. and Matsuda, F. (1988). A mathematical modeling of flow and temperature fields in gas‐tungsten‐arc. Journal of The Japan Welding Society 6 (1): 91–98.

4 4 McKelliget, J. and Szekely, J. (1986). Heat transfer and fluid flow in the welding arc. Metallurgical Transactions A 17 (7): 1139–1148.

5 5 Choo, R.T.C., Szekely, J., and Westhoff, R.C. (1990). Modeling of high‐current arcs with emphasis on free surface phenomena in the weld pool. Welding Journal 69 (9): 346s–361s.

6 6 Lee, S.Y. and Na, S.J. (1996). A numerical analysis of a stationary gas tungsten welding arc considering various electrode angles. Welding Journal 75 (9): 269s–279s.

7 7 Tanaka, M., Yamamoto, K., Tashiro, S. et al. (2010). Time‐dependent calculations of molten pool formation and thermal plasma with metal vapour in gas tungsten arc welding. Journal of Physics D: Applied Physics 43 (43): 434009.

8 8 Kodama, S., Sugiura, K., Nakanishi, S. et al. (2013). Effect of plasma heat source characteristics on nitrogen absorption in gas tungsten arc weld metal. Welding in the World 57 (6): 925–932.

9 9 Murphy, A.B. (2010). The effects of metal vapour in arc welding. Journal of Physics D: Applied Physics 43 (43): 434001.

10 10 Murphy, A.B. (2011). A self‐consistent three‐dimensional model of the arc, electrode and weld pool in gas–metal arc welding. Journal of Physics D: Applied Physics 44 (19): 194009.

11 11 Murphy, A.B. (2013). Influence of metal vapour on arc temperatures in gas–metal arc welding: convection versus radiation. Journal of Physics D: Applied Physics 46 (22): 224004.

12 12 Murphy, A.B. (2013). Influence of droplets in gas–metal arc welding: new modelling approach, and application to welding of aluminium. Science and Technology of Welding and Joining 18 (1): 32–37.

13 13 Murphy, A.B., Nguyen, V., Feng, Y. et al. (2017). A desktop computer model of the arc, weld pool and workpiece in metal inert gas welding. Applied Mathematical Modelling 44: 91–106.

14 14 Nestor, O.H. (1962). Heat intensity and current density distributions at the anode of high current, inert gas arcs. Journal of Applied Physics 33 (5): 1638–1648.

15 15 Schoeck, P.A. (1963). An investigation of the anode energy balance of high intensity arcs in argon. In: Modern Developments in Heat Transfer, 353–400.

16 16 Tsai, N. (1983). Heat Distribution and Weld Bead Geometry in Arc Welding. Cambridge, MA: Department of Materials Science and Engineering. Massachusetts Institute of Technology.

17 17 Lu, M. and Kou, S. (1988). Power and current distributions in gas tungsten arcs. Welding Journal 67 (2): 29s–34s.

18 18 Lawson, W.H.S. and Kerr, H.W. (1976). Fluid motion in gta weld pools. Part 2 ‐ weld pool shapes. Welding Research International 6 (6): 1–17.

19 19 Lin, M.L. and Eagar, T.W. (1985). Influence of arc pressure on weld pool geometry. Welding Journal 64 (6): 163s–169s.

20 20 Matsunawa, A. and Yokoya, S. (1990). Fluid flow and its effect on penetration shape in stationary arc welds. In: Recent Trends in Welding Science and Technology, 31–35. Materials Park, Ohio: ASM International.

21 21 Kou, S. (1996). Transport Phenomena in Materials Processing, 3–115. New York: John Wiley and Sons.

22 22 Oreper, G.M., Eagar, T.W., and Szekely, J. (1983). Convection in arc weld pools. Welding Journal 62 (11): 307s–312s.

23 23 Kou, S. and Sun, D.K. (1985). Fluid flow and weld penetration in stationary arc welds. Metallurgical and Materials Transactions A 16 (1): 203–213.

24 24 Kou, S. and Wang, Y.H. (1986). Weld pool convection and its effect. Welding Journal 65 (3): 63s–70s.

25 25 Kou, S. and Wang, Y.H. (1986). Three‐dimensional convection in laser melted pools. Metallurgical Transactions A 17 (12): 2265–2270.

26 26 Kou, S. and Wang, Y.H. (1986). Computer simulation of convection in moving arc weld pools. Metallurgical Transactions A 17A: 2271.

27 27 Heiple, C.R. and Roper, J.R. (1982). Mechanism for minor element effect on GTA fusion zone geometry. Welding Journal 61 (4): 97s–102s.

28 28 Heiple, C.R. and Roper, J.R. (1982). Trends in Welding Research in the United States (ed. S.A. David), 489–520. Metals Park, OH: American Society for Metals.

29 29 Heiple, C.R., Roper, J.R., Stagner, R.T., and Aden, R.J. (1983). Surface active element effects on the shape of GTA, laser and electron beam welds. Welding Journal 62 (3): 72s–77s.

30 30 Heiple, C.R., Burgardt, P., and Roper, J.R. (1983). The effect of trace elements on GTA weld penetration. In: Modeling of Casting and Welding Processes II, 193–205. Warrendale, PA: TMS AIME.

31 31 Heiple, C.R. and Burgardt, P. (1985). Effects of SO2 shielding gas additions on GTA weld shape. Welding Journal 64 (6): 159s–162s.

32 32 Kou, S., Limmaneevichitr, C., and Wei, P.S. (2011). Oscillatory Marangoni flow: a fundamental study by conduction‐mode laser spot welding. Welding Journal 90 (12): 229‐s–240‐s.

33 33 Keene, B.J., Mills, K.C., and Brooks, R.F. (1985). Surface properties of liquid metals and their effects on weldability. Materials Science and Technology 1 (7): 569–571.

34 34 Limmaneevichitr, C., and Kou, S. (2000). Unpublished research. University of Wisconsin, Madison, WI.

35 35 Sahoo, P., DebRoy, T., and McNallan, M.J. (1988). Surface tension of binary metal—surface active solute systems under conditions relevant to welding metallurgy. Metallurgical and Materials Transactions B 19 (3): 483–491.

36 36 McNallan, M.J. and Debroy, T. (1991). Effect of temperature and composition on surface tension in Fe‐Ni‐Cr alloys containing sulfur. Metallurgical and Materials Transactions B 22 (4): 557–560.

37 37 Pitscheneder, W., DebRoy, T., Mundra, K., and Ebner, R. (1996). Role of sulfur and processing variables on the temporal evolution of weld pool geometry during multikilowatt laser beam welding of steels. Welding Journal 75 (3): 71s–80s.

38 38 Sundell, R.E., Correa, S.M., Harris, L.P., Solomon, H.D., Wojcik, L.A., Savage, W.F., Walsh, D.W., and Lo, G.D., General Electric Report No. 86SRD013. 1986, General Electric Company: Schenectady, NY.

39 39 Zacharia, T., David, S.A., Vitek, J.M., and Debroy, T. (1989). Weld pool development during GTA and laser beam welding of type 304 stainless steel, part II—experimental correlation. Welding Journal 68 (12): 510s–519s.

40 40 Limmaneevichitr, C. and Kou, S. (2000). Visualization of Marangoni convection in simulated weld pools. Welding Journal 79 (5): 126s–135s.

41 41 Mazumder, J. and Voekel, D. (1992). Challenges in modeling and measurement of laser materials processing. In: Laser Advanced Materials Processing –Science and Applications (eds. A. Matsunawa and S. Katayama), 373–380. Osaka, Japan: High Temperature Society of Japan.

42 42 Tsai, M.C. and Kou, S. (1989). Marangoni convection in weld pools with a free surface. International Journal for Numerical Methods in Fluids 9 (12): 1503–1516.

43 43 Limmaneevichitr, C. and Kou, S. (2000). Visualization of Marangoni convection in simulated weld pools containing a surface‐active agent. Welding Journal 79 (11): 324s–330s.

44 44 Smechenko, V.K. and Shikobalova, L.P. (1947). Surface tension and crystallization: surface tension of molten salt solutions. Zhurnal Fizicheskoi Khimii 21: 613–622.

45 45 Mishra, S., Lienert, T.J., Johnson, M.Q., and DebRoy, T. (2008). An experimental and theoretical study of gas tungsten arc welding of stainless steel plates with different sulfur concentrations. Acta Materialia 56 (9): 2133–2146.

46 46 Tsai, M.C. and Kou, S. (1990). Electromagnetic‐force‐induced convection in weld pools with a free surface. Welding Journal 69 (6): 241s–246s.

47 47 Flemings, M.C. (1974). Solidification Processing. New York: McGraw‐Hill.

48 48 Tsai, M.C. and Kou, S. (1990). Weld pool convection and expansion due to density variations. Numerical Heat Transfer 17 (1): 73–89.

49 49 Choo, R.T.C. and Szekely, J. (1994). The possible role of turbulence in GTA weld pool behavior. Welding Journal 73 (2): 25s–31s.

50 50 Weckman, D.C. (1999). Trends in Welding Research, 3–12. Materials Park: ASM International, OH.

51 51 Hong, K., Weckman, D.C., Strong, A.B., and Zheng, W. (2002). Modelling turbulent thermofluid flow in stationary gas tungsten arc weld pools. Science and Technology of Welding and Joining 7 (3): 125–136.

52 52 Hong, K., Weckman, D.C., Strong, A.B., and Zheng, W. (2003). Vorticity based turbulence model for thermofluids modelling of welds. Science and Technology of Welding and Joining 8 (5): 313–324.

53 53 Kou, S. (2012). Fluid flow and solidification in welding: three decades of fundamental research at the University of Wisconsin. Welding Journal 91 (11): 287s–302s.

54 54 Xiao, Y. and Den Ouden, G. (1990). A study of GTA weld pool oscillation. Welding Journal 69 (8): 289s–293s.

55 55 Xiao, Y.H. and Den Ouden, G. (1993). Weld pool oscillation during GTA welding of mild steel. Welding Journal 72: 428s–434s.

56 56 Howse, D.S. and Lucas, W. (2000). Investigation into arc constriction by active fluxes for tungsten inert gas welding. Science and Technology of Welding and Joining 5 (3): 189–193.

57 57 Tanaka, M., Shimizu, T., Terasaki, T. et al. (2000). Effects of activating flux on arc phenomena in gas tungsten arc welding. Science and Technology of Welding and Joining 5 (6): 397–402.

58 58 Kuo, M., Sun, Z., and Pan, D. (2001). Laser welding with activating flux. Science and Technology of Welding and Joining 6 (1): 17–22.

59 59 Yu, P. and Kou, S. Research in Progress. Madison, WI: University of Wisconsin.

60 60 Wei, P.S., Wang, S.C., and Lin, M.S. (1996). Transport phenomena during resistance spot welding. Journal of Heat Transfer 118 (3): 762–773.

61 61 Wei, P.S. and Wu, T.H. (2010). Effects of electrical current on transport processes in resistance spot welding. Science and Technology of Welding and Joining 15 (6): 448–456.

62 62 Wei, P.S. and Wu, T.H. (2011). Magnetic property effect on transport processes in resistance spot welding. Journal of Physics D: Applied Physics 44 (32): 325501.

63 63 Wei, P.S. and Wu, T.H. (2012). Electrical contact resistance effect on resistance spot welding. International Journal of Heat and Mass Transfer 55 (11): 3316–3324.

64 64 Wei, P.S. and Wu, T.H. (2013). Numerical study of electrode geometry effects on resistance spot welding. Science and Technology of Welding and Joining 18 (8): 661–670.

65 65 Wei, P.S. and Wu, T.H. (2014). Effects of electrode contact condition on electrical dynamic resistance during resistance spot welding. Science and Technology of Welding and Joining 19 (2): 173–180.

66 66 Yao, Q., Luo, Z., Li, Y. et al. (2014). Effect of electromagnetic stirring on the microstructures and mechanical properties of magnesium alloy resistance spot weld. Materials & Design 63: 200–207.

67 67 Li, Y., Lin, Z., Shen, Q., and Lai, X. (2011). Numerical analysis of transport phenomena in resistance spot welding process. Journal of Manufacturing Science and Engineering 133 (3): 031019.

68 68 Li, Y.B., Shen, Q., Lin, Z., and Hu, S.J. (2011). Quality improvement in resistance spot weld of advanced high strength steel using external magnetic field. Science and Technology of Welding and Joining 16 (5): 465–469.

69 69 Li, Y.B., Li, Y.T., Shen, Q., and Lin, Z.Q. (2013). Magnetically assisted resistance spot welding of dual‐phase steel. Welding Journal 92 (4): 124s–132s.

70 70 Li, Y., Luo, Z., Yan, F. et al. (2014). Effect of external magnetic field on resistance spot welds of aluminum alloy. Materials & Design (1980–2015) 56: 1025–1033.

71 71 Li, Y., Zhang, Y., Bi, J., and Luo, Z. (2015). Impact of electromagnetic stirring upon weld quality of Al/Ti dissimilar materials resistance spot welding. Materials & Design 83: 577–586.

72 72 Lu, S., Fujii, H., and Nogi, K. (2008). Marangoni convection and weld shape variations in He–CO2 shielded gas tungsten arc welding on SUS304 stainless steel. Journal of Materials Science 43 (13): 4583–4591.