Geodesic
Mathematical model of hydrodynamics and heat transfer of the melted steel in a ladle furnace while arc heating is performed
Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 129-136.

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Mathematical model of hydrodynamics and heat transfer of the melted steel is presented in this article. The main improvements of the model are its three-dimensionality and taking into account of compressibility of the gas-liquid continuum. Given the visualization of the results, which were obtained in programs in C++ language, those are the implementation of the model.
Keywords: gas-liquid continuum, hydrodynamics, heat transfer, mathematical modeling, arc heating. 
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D. U. Kabakov; S. E. Samokhvalov; V. P. Piptyuk. Mathematical model of hydrodynamics and heat transfer of the melted steel in a ladle furnace while arc heating is performed. Matematičeskoe modelirovanie, Tome 26 (2014) no. 4, pp. 129-136. http://geodesic.mathdoc.fr/item/MM_2014_26_4_a10/

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[2] Kabakov D. Yu., Samokhvalov S. Є., “Spryazheni protsesi gidrodinamiki ta teploperenosu u kovshi pid chas napovnennya”, Sistemni tekhnologiï, 2012, no. 2 (79), 146–151 http://archive.nbuv.gov.ua/portal/natural/syte/2012_2/19.pdf

[3] Okhotskii V. B., Voityuk K. V., Shibko A. V., “Issledovanie protsessa produvki metalla v kovshe argonom”, Izv. vuzov. Chernaya metallurgiya, 1991, no. 1, 17–19

[4] Piptyuk V. P., Polyakov V. F., Logozinskii I. N. i dr., “Osnovnye dannye dlya chislennykh issledovanii gidrodinamiki vanny na ustanovkakh kovsh-pech peremennogo toka raznoi moschnosti”, Sb. nauch. tr. IChM NANU, Fundamentalnye i prikladnye problemy chernoi metallurgii, 14, 2007, 145–153 http://archive.nbuv.gov.ua/portal/natural/Ftpp/2007-14/14-07/14145.pdf