Geodesic
Mathematical modeling of the mono crystal growth by Czochralski tube method
Matematičeskoe modelirovanie, Tome 5 (1993) no. 7, pp. 10-16.

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This paper deals with the conjugated problem of crystal growth by Czochralski tube method. The radius of the crystal is assumed to be equal to that of the tube. The velocity field in the melt, the shape of the solidification isotherm and the temperature distribution in both phases are calculated simultaneously. Diffusive heat transfer in the tube, crystal and tube rotation are taken into account. Crystalization regimes are proposed for which the solidification front has slight curvature and it is convex toward the melt. 
@article{MM_1993_5_7_a1,
     author = {M. P. Marchenko},
     title = {Mathematical modeling of the mono crystal growth by {Czochralski} tube method},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {10--16},
     publisher = {mathdoc},
     volume = {5},
     number = {7},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1993_5_7_a1/}
}
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M. P. Marchenko. Mathematical modeling of the mono crystal growth by Czochralski tube method. Matematičeskoe modelirovanie, Tome 5 (1993) no. 7, pp. 10-16. http://geodesic.mathdoc.fr/item/MM_1993_5_7_a1/