MODELING OF COMBINED NATURAL/THERMOCAPILLARY CONVECTION FLOWS IN GERMANIUM MELT AT HIGH TEMPERATURES

Year 2018, Volume: 8 Issue: 1.1, 193 - 207, 01.09.2018

F. Mechighel N. Armour S. Dost

Abstract

A mathematical model for the description of combined natural/ thermocap- illary convection melt ows in cylindrical 3D geometry is developed. It is utilized to model germanium melt convective ows in an isothermal experimental crucible setup. This experimental setup is devised exclusively to study the dissolution phenomenon of silicon into germanium melt. In this system, the germanium melt is subjected to higher temperatures. Using a simplied axisymmetric 2D model, numerical simulations are carried out to examine the combined natural/thermocapillary ows developing in the ger-manium melt. Pure thermocapillary and pure natural convective ows are also studied numerically.

Keywords

Germanium melt, free surface, Marangoni convection, natural thermal or buoyant convection, mathematical modeling, numerical simulation.

References

• Kasper, E., Paul, D.J., (2005), Springer-Verlag Berlin.
• Dost, S., Lent, B. (2007), Elsevier, Amsterdam, the Netherlands.
• Armour, N., Yildiz, M., Yildiz, E., Dost, S. (2008), ECS Transactions, 16, pp. 135146.
• Prasad, V., Zhang, H., Anselmo A.P. (1997), In Advances in heat transfer, Acad. Press, 30, pp. 435.
• Bohm, J., Ludge, A., Schroder, W., (1994), Chap. 4. In: Handbook of Crystal Growth, Vol. 2A
• D.T.J. Hurle (ed.), Elsevier, North-Holland. Van der Eerden J.P., (1993), Chap. 6. In Handbook of Crystal Growth, Vol. 1A, ed. By Hurle, D.T.J.
• Elsevier, North-Holland. Bliss, D.F. (2010), Chapter 7. Part B, p. 207, in Springer Handbook of Crystal Growth, G. Dhanaraj
• K. Byrappa, V. Prasad, M. Dudley (Eds.), Springer-Verlag Berlin. Nishijima, Y., Nakajima, K., Otsubo, K., Ishikawa, H., (2000), J. Cryst. Growth, 208, pp. 171178.
• Kuhlmann, H.C., (1999), Springer-Verlag Berlin Heidelberg.
• Kakimoto K., (2004), Crystal Growth - from Fundamentals to Technology. Muller, G.; Metois J.-J. and Rudolph P. (Editors), Elsevier, Amsterdam.
• Armour, N., Dost, S. (2009), J. Cryst. Growth, 311, pp. 780782.
• Armour, N., Dost, S., Lent, B., (2007), J. Cryst. Growth, 299, pp. 227233.
• Sampath, R., Zabaras, N., (2001), J. Comp. Physics, 168, pp. 384411.
• Yildiz, M., (2005), PhD thesis, University of Victoria, Canada.
• COMSOL Multiphysics Modeling Guide (2008).
• Mechighel, F., Armour, N., Dost, S., Kadja, M., (2014), CMES: Computer Modeling in Engineering and Sciences, 97(1), pp.5380.
• Mechighel, F., Armour, N., Dost, S., Kadja, M., (2011), TWMS J. App. Eng. Math., 1(2), pp. 200-222.