Verified reduction of a model for a continuous casting process

Lewis, 1998, A correlation to describe interfacial heat transfer during solidification simulation and its use in the optimal feeding design of castings, Metall. Mater. Trans. B, 29, 437, 10.1007/s11663-998-0122-y Lee, 2000, Prediction of cracks in continuously cast steel beam blank through fully coupled analysis of fluid flow, heat transfer, and deformation behavior of a solidifying shell, Metall. Mater. Trans. A, 31, 225, 10.1007/s11661-000-0067-5 Aboutalebi, 1995, Coupled turbulent flow, heat and solute transport in continuous casting processes, Metall. Mater. Trans. B, 26, 731, 10.1007/BF02651719 Aboutalebi, 1995, Numerical study of coupled turbulent flow and solidification for steel slab casters, Numer. Heat Trans. A, 28, 279, 10.1080/10407789508913746 Mahmoudi, 2001, Modelling of fluid flow, heat transfer, solidification in the strip casting of copper base alloy. Part 3. Solidification – a theoretical study, Scand. J. Metall., 30, 136, 10.1034/j.1600-0692.2001.300304.x Mahmoudi, 2003, An experimental and numerical study on the modelling of fluid flow, heat transfer and solidification in a copper continuous strip casting process, Mater. Trans., 44, 1741, 10.2320/matertrans.44.1741 Zhang, 2012, Computational fluid dynamics modeling: application to transport phenomena during the casting process, JOM, 64, 1059, 10.1007/s11837-012-0419-9 Mahmoudi, 2006, Mathematical modelling of fluid flow, heat transfer and solidification in a strip continuous casting process, Int. J. Cast Metals Res., 19, 223, 10.1179/136404606225023453 Yao, 2005, Monitoring and analysis of local mould thermal behaviour in continuous casting of round billets, Ironmak. Steelmak., 32, 359, 10.1179/174328105X28847 Yao, 2004, Real-time analysis on non-uniform heat transfer and solidification in mould of continuous casting round billets, ISIJ Int., 44, 1696, 10.2355/isijinternational.44.1696 Lee, 1999, A fully coupled analysis of fluid flow, heat transfer and stress in continuous round billet casting, ISIJ Int., 39, 435, 10.2355/isijinternational.39.435 Amin, 1999, Conjugate heat transfer during two-phase solidification process in a continuously moving metal using average heat capacity method, Int. J. Heat Mass Transf., 42, 2883, 10.1016/S0017-9310(98)00366-4 Das, 1996, Computational modelling of thermal transport phenomena in continuous casting process based on non-orthogonal control volume approach, Commun. Numer. Methods Eng., 12, 657, 10.1002/(SICI)1099-0887(199610)12:10<657::AID-CNM13>3.0.CO;2-Z Vynnycky, 2009, An asymptotic model for the formation and evolution of air gaps in vertical continuous casting, Proc. R. Soc. A, 465, 1617, 10.1098/rspa.2008.0467 Vynnycky, 2010, Air gaps in vertical continuous casting in round moulds, J. Eng. Maths, 68, 129, 10.1007/s10665-009-9341-8 Vynnycky, 2009, A mathematical model for air-gap formation in vertical continuous casting: the effect of superheat, Trans. Ind. Inst. Metals, 62, 495, 10.1007/s12666-009-0064-3 Vynnycky, 2013, On the onset of air-gap formation in vertical continuous casting with superheat, Int. J. Mech. Sci., 73, 69, 10.1016/j.ijmecsci.2013.04.007 Florio, 2015, Mould-taper asymptotics and air gap formation in continuous casting, Appl. Math. Comput., 268, 1122 Florio, 2017, On the interactive effects of mould taper and superheat on air gaps in continuous casting, Acta Mechanica, 228, 233, 10.1007/s00707-016-1717-z Teskeredžić, 2015, Numerical method for calculation of complete casting processes-part I: theory, Numer. Heat Trans. B, 68, 295, 10.1080/10407790.2015.1033296 Teskeredžić, 2015, Numerical method for calculation of complete casting processes-part II: validation and application, Numer. Heat Trans. B, 68, 317, 10.1080/10407790.2015.1033325 Bailey, 1996, Multiphysics modelling of the metals casting process, Proc. R. Soc. A, 452, 459, 10.1098/rspa.1996.0024 Teskeredžić, 2002, Numerical method for heat transfer, fluid flow, and stress analysis in phase-change problems, Numer. Heat Trans. B, 42, 437, 10.1080/10407790190054021 Koric, 2010, Multiphysics model of metal solidification on the continuum level, Numer. Heat Trans. B, 58, 371, 10.1080/10407790.2011.540954 Mitchell, 2014, On the numerical solution of two-phase Stefan problems with heat-flux boundary conditions, J. Comput. Appl. Maths, 264, 49, 10.1016/j.cam.2014.01.003 Mitchell, 2012, An accurate finite-difference method for ablation-type Stefan problems, J. Comput. Appl. Math., 236, 4181, 10.1016/j.cam.2012.05.011 Mitchell, 2016, On the accurate numerical solution of a two-phase Stefan problem with phase formation and depletion, J. Comput. Appl. Math., 300, 259, 10.1016/j.cam.2015.12.021 Mitchell, 2011, An accurate numerical solution for the transient heating of an evaporating spherical droplet, Appl. Math. Comput., 217, 9219 Vynnycky, 2010, On the solution of Stefan problems with delayed onset of phase change, 1404 Mitchell, 2006, Analysis of box schemes for reactive flow problems, SIAM J. Sci. Comput., 27, 1202, 10.1137/030601910 Chatterjee, 2000, A full 3-dimensional adaptive finite volume scheme for transport and phase-change processes, part I: formulation and validation, Numer. Heat Trans. A, 37, 801, 10.1080/10407780050045847 Del Borrello, 2003, Numerical simulation of the liquid flow into a porous medium with phase change: application to metal matrix composites processing, Numer. Heat Trans. A, 44, 723, 10.1080/716100518 Pokorny, 2008, Prediction of hot tear formation in a magnesium alloy permanent mold casting, Int. J. Metalcasting, 2, 41, 10.1007/BF03355435 Pardeshi, 2009, Modeling of solidification process in a rotary electromagnetic stirrer, Numer. Heat Trans. A, 55, 42, 10.1080/10407780802553961 Shamsi, 2007, Three dimensional turbulent fluid flow and heat transfer mathematical model for the analysis of a continuous slab caster, ISIJ Int., 47, 433, 10.2355/isijinternational.47.433 Moraga, 2010, Study of convective non-Newtonian alloy solidification in molds by the PSIMPLER/finite-volume method, Numer. Heat Trans. A, 57, 936, 10.1080/10407782.2010.490171 Vynnycky, 2013, On the role of radiative heat transfer in air gaps in vertical continuous casting, Appl. Math. Model., 37, 2178, 10.1016/j.apm.2012.05.005 Kelly, 1988, Initial development of thermal and stress fields in continuously cast steel billets, Metall. Mater. Trans. A, 19A, 2589, 10.1007/BF02645486 O’Connor, 1994, Modeling the thin-slab continuous-casting mold, Metall. Mater. Trans. B, 25, 443, 10.1007/BF02663395 Cebeci, 1984 Cebeci, 1977 Cebeci, 2005 Mitchell, 2009, Finite-difference methods with increased accuracy and correct initialization for one-dimensional Stefan problems, Appl. Math. Comput., 215, 1609 Strikwerda, 2004 Koric, 2010, Enhanced latent heat method to incorporate superheat effects into fixed-grid multiphysics simulations, Numer. Heat Trans. B, 57, 396, 10.1080/10407790.2010.496657