Funct. Mater. 2014; 21 (1): 92-104.

Complex heat transfer at directed crystallization of semitransparent materials

V.I.Deshko[1], A.Ya.Karvatskii[1], A.M.Kudin[2], I.V. Lokhmanets[1]

[1] Heat Engineering Dept., National Technical University "Kiev Polytechnic Institute", 37 Peremogy Ave., 03056 Kiev, Ukraine
[2] Institute for Scintillation Materials, STC "Institute for Single Crystals", National Academy of Sciences of Ukraine, 60 Lenin Ave., 61001 Kharkiv, Ukraine


The sensibility of thermal regimes at crystal-melt system to inner or outer parameters was studied for semitransparent media by the numerical simulation of complex heat transfer. A model of radiation-convective and radiation-conductive heat transfer was developed. Advanced features of the model, such as dynamic evolution of interface, were realized by implementation of user-defined functions. The 2D axisymmetric model is limited geometrically to the cylindrical crystal-melt system since heat regimes and temperature gradients in the area near crystallization front are the most important. Combined effect of radiation, convective and conductive heat transfer mechanisms on the formation of temperature fields and heat flows, position and shape of the crystallization front and distribution of the temperature gradients in the crystal-melt system have been examined for the oxide and alkali-halide classes of semitransparent materials at different growth conditions, considering selectivity of their absorption. Analysis of the results allowed developing the recommendations for approximation of the effects of radiation and convection heat transfer and their interaction. This allows justification of several possible simplifying approaches at development of the numerical models of crystal growth furnaces, including on-line models for operative control of the growth process.


1. C.W.Lan, Chem. Engin. Sci., 59, 1437 (2004).

2. V.V.Kalayev, Yu.N.Makarov, V.S.Yuferev, A.I.Zhmakin, in: Crystal Growth Technology: From Fundamentals and Simulation to Large-Scale Production, ed. by H.J.Scheel and P.Capper, New York, Wiley-VCH (2007).

3. M.Abrams, R.Viskanta, J. Heat Transfer, 96, 184 (1974).

4. R.Viskanta, E.E.Anderson, Adv. Heat Transfer, 11, 317 (1975).

5. Q.Xiao, J.J.Derby, J. Cryst. Growth, 128, 188 (1993).

6. A.Yeckel, J.J.Derby, J. Electron. Mater., 33, 1 (2004).

7. V.S.Yuferev, O.N.Budenkova, M.G.Vasiliev et al., J. Cryst. Growth, 253, 383 (2003).

8. A.Hayashi, M.Kobayashi, Ch.Jing et al., Int. J. Heat Mass Transfer, 47, 5501 (2004).

9. Z.Galazka, H.Wilke, J. Cryst. Res. Techn., 35, 1263 (2000).<1263::AID-CRAT1263>3.0.CO;2-Z

10. A.Voigt, C.Weichmann, J.Nitschkowski et al., J. Cryst. Research Technology, 37, 77 (2002).<77::AID-CRAT77>3.0.CO;2-K

11. I.Yu.Evstratov, V.V.Kalaev, A.I.Zhmakin et al., J. Crystal Growth, 230, 22 (2001).

12. V.V.Kalaev, A.I.Zhmakin, E.M.Smirnov, J. Turbulence, 3, 1 (2002).

13. A.V.Kolesnikov, V.I.Deshko, Yu.V.Lokhmanets, Functional Materials, 17, 483 (2010).

14. K.Lin, P.Dold, J. Cryst. Res. Technology, 36, 629 (2001).<629::AID-CRAT629>3.0.CO;2-7

15. A.Yeckel, J.J.Derby, Bulk Crystal Growth of Electronic, Optical and Optoelectronic Materials, New-York, Wiley (2005).

16. V.I.Deshko, V.D.Golyshev, A.Ya.Karvatskii et al., Functional Materials, 15, 90 (2008).

17. V.I.Deshko, A.Ya.Karvatskii, A.V.Lenkin, Yu.V.Lokhmanets, Functional Materials, 15, 229 (2008).

18. ANSYS FLUENT 12.0 Documentation (2009).

19. S.V.Bykova, V.D.Golyshev, M.A.Gonik et al., J. Cryst. Growth, 266, 247 (2004).

20. H.K.Versteeg, W.Malalasekera, An Introduction to Computational Fluid Dynamics: The Finite Volume Method, 2nd ed., Prentice Hall, Harlow, England (2007).

21. J.Y.Murthy, S.R.Mathur, A Finite Volume Method For Radiative Heat Transfer Using Unstructured Meshes, AIAA-98-0860 (1998).

22. S.A.Orszag, V.Yakhot, W.S.Flannery et al., in: Int. Conf. Near-Wall Turbulent Flows, Tempe, Arizona (1993).

Current number: