Analysis of the heat transfer coefficients of the whole process of continuous casting of carbon steel

  • Tarquínio Plynio Durães dos Anjos
  • Paulo Vicente de Cassia Lima Pimenta
  • Francisco Marcondes
Technical Paper


In this work, we use a numerical–experimental approach which is based on the solution of the inverse heat conduction problem (IHCP) and temperature measurements. To obtain the profile of the heat transfer coefficients for all stages of the industrial manufacture of continuous casting process, we evaluate the three cooling regions. At primary ones, we use the temperature measured at the wall of the mold by thermocouples and the surface temperature of the ingot in the secondary and tertiary regions by optical pyrometers placed at the strategic positions. The IHCP procedure analysis the behavior of the numerical heat transfer coefficient under several conditions, such as casting temperature and speed as well as the chemical composition of the steel. We also propose a correlation to evaluate the overall heat transfer coefficient profile as function of the investigated parameters.


Continuous casting Heat transfer coefficient Numerical–experimental approach Ingot solidification 



Paulo Vicente de Cassia Lima Pimenta would like to thank CAPES (Coordination for the Improvement of Higher Education Personnel and Gerdau Cearense) for financial support of this work.


  1. 1.
    Santos CA, Spim JA, Garcia A (2003) Mathematical modeling and optimization strategies (genetic algorithm and knowledge base) applied to the continuous casting of steel. Eng Appl Artif Intell 16(5):511–527CrossRefGoogle Scholar
  2. 2.
    Das SK (1999) Thermal modelling of DC continuous casting including submould boiling heat transfer. Appl Therm Eng 19(8):897–916CrossRefGoogle Scholar
  3. 3.
    Saraswat R, Maijer DM, Lee PD, Mills KC (2007) The effect of mould flux properties on thermo-mechanical behaviour during billet continuous casting. ISIJ Int 47(1):95–104CrossRefGoogle Scholar
  4. 4.
    Vynnycky M (2013) On the onset of air-gap formation in vertical continuous casting with superheat. Int J Mech Sci 73:69–76CrossRefGoogle Scholar
  5. 5.
    Janik M, Dyja H, Berski S, Banaszek G (2004) Two-dimensional thermomechanical analysis of continuous casting process. J Mater Process Technol 153:578–582CrossRefGoogle Scholar
  6. 6.
    Pinheiro CA, Samarasekera IV, Brimacomb JK, Walker BN (2000) Mould heat transfer and continuously cast billet quality with mould flux lubrication Part 1 Mould heat transfer. Ironmak Steelmak 27(1):37–54CrossRefGoogle Scholar
  7. 7.
    Huang X, Thomas BG (1998) Modeling of transient flow phenomena in continuous casting of steel. Can Metall Q 37(3–4):197–212CrossRefGoogle Scholar
  8. 8.
    Brimacombe JK, Samarasekera IV (1994) The challenge of thin slab casting. Iron Steelmak 21(11):29–39Google Scholar
  9. 9.
    Mizikar EA (1970) Spray-cooling investigation for continuous casting of billets and blooms. Iron Steel Eng 47(6):53–60Google Scholar
  10. 10.
    de Barcellos VK, Ferreira CR, Dos Santos CA, Spim JA (2013) Analysis of metal mould heat transfer coefficients during continuous casting of steel. Ironmak Steelmak 37(1):47–56CrossRefGoogle Scholar
  11. 11.
    Pascon F, Habraken AM (2007) Finite element study of the effect of some local defects on the risk of transverse cracking in continuous casting of steel slabs. Comput Methods Appl Mech Eng 196(21):2285–2299CrossRefMATHGoogle Scholar
  12. 12.
    Wolf M, Kurz W (1981) The effect of carbon content on solidification of steel in the continuous casting mold. Metall Trans B 12(1):85–93CrossRefGoogle Scholar
  13. 13.
    Garcia A, Prates M (1983) The application of a mathematical model to analyze ingot thermal behavior during continuous casting. In: Proceedings of the fourth IFAC symposium, vol 16, no 15. Helsinki, Finland, pp 273–279Google Scholar
  14. 14.
    Hills AW (1965) Simplified theoretical treatment for transfer of heat in continuous-casting machine moulds. J Iron Steel Inst 203:18Google Scholar
  15. 15.
    Cheung N, Garcia A (2001) The use of a heuristic search technique for the optimization of quality of steel billets produced by continuous casting. Eng Appl Artif Intell 14(2):229–238CrossRefGoogle Scholar
  16. 16.
    Wang X, Kong L, Du F, Yao M, Zhang X, Ma H, Wang Z (2016) Mathematical modeling of thermal resistances of mold flux and air gap in continuous casting mold based on an inverse problem. ISIJ Int 56(5):803–811CrossRefGoogle Scholar
  17. 17.
    Krishnan M, Sharma DG (1996) Determination of the interfacial heat transfer coefficient h in unidirectional heat flow by Beck’s non linear estimation procedure. Int Commun Heat Mass Transf 23(2):203–214CrossRefGoogle Scholar
  18. 18.
    Kumar TP, Prabhu KN (1991) Heat flux transients at the casting/chill interface during solidification of aluminum base alloys. Metall Trans B 22(5):717–727CrossRefGoogle Scholar
  19. 19.
    Beck JV (1988) Combined parameter and function estimation in heat transfer with application to contact conductance. J Heat Transf 110(4b):1046–1058CrossRefGoogle Scholar
  20. 20.
    Ho K, Pehlke RD (1985) Metal-mold interfacial heat transfer. Metall Trans B 16(3):585–594CrossRefGoogle Scholar
  21. 21.
    Beck JV (1970) Nonlinear estimation applied to the nonlinear inverse heat conduction problem. Int J Heat Mass Transf 13(4):703–716CrossRefGoogle Scholar
  22. 22.
    Maliska CR (2004) Heat transfer and computational fluid mechanics, Florianópolis, 2ª edn. Editora LTC. (In Portuguese)Google Scholar
  23. 23.
    Patankar SV. Numerical heat transfer and fluid flow: computational methods in mechanics and thermal scienceGoogle Scholar
  24. 24.
    Demirdžić I (2016) A fourth-order finite volume method for structural analysis. Appl Math Model 40(4):3104–3114MathSciNetCrossRefGoogle Scholar
  25. 25.
    Filippini G, Maliska CR, Vaz M (2014) A physical perspective of the element-based finite volume method and FEM-Galerkin methods within the framework of the space of finite elements. Int J Numer Methods Eng 98(1):24–43MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Vaz M, Muñoz-Rojas PA, Filippini G (2009) On the accuracy of nodal stress computation in plane elasticity using finite volumes and finite elements. Comput Struct 87(17):1044–1057CrossRefGoogle Scholar
  27. 27.
    Marcondes F, Santos LO, Varavei A, Sepehrnoori K (2013) A 3D hybrid element-based finite-volume method for heterogeneous and anisotropic compositional reservoir simulation. J Petrol Sci Eng 31(108):342–351CrossRefGoogle Scholar
  28. 28.
    Slone AK, Pericleous K, Bailey C, Cross M (2002) Dynamic fluid–structure interaction using finite volume unstructured mesh procedures. Comput Struct 80(5):371–390CrossRefGoogle Scholar
  29. 29.
    Garcia A (2001) Solidificação: Fundamentos e Aplicações, editora da Unicamp. São Paulo, Brasil, pp 201–242Google Scholar
  30. 30.
    Spinelli JE, Tosetti JP, Santos CA, Spim JA, Garcia A (2004) Microstructure and solidification thermal parameters in thin strip continuous casting of a stainless steel. J Mater Process Technol 150(3):255–262CrossRefGoogle Scholar
  31. 31.
    Monrad, Pelton, Gnielinski and Florenko (2003) Cia Europa Metalli, Manual Técnico v. único, pp 44–65Google Scholar
  32. 32.
    Bolle E, Moureau JC (1946) Sprays cooling of hot surfaces: a description of the dispersed phase and a parametric study of heat transfer results. Proc Two Phase Flows Heat Transf 101:1327–1346Google Scholar
  33. 33.
    Brimacombe JK, Samarasekera IV, Lait JE (1984) Continuous casting: heat flow, solidification and crack formation., vol 2. Iron and Steel Society of AIMEGoogle Scholar
  34. 34.
    Mahapatra RB, Brimacombe JK, Samarasekera IV (1991) Mold behavior and its influence on quality in the continuous casting of steel slabs: part II. Mold heat transfer, mold flux behavior, formation of oscillation marks, longitudinal off-corner depressions, and subsurface cracks. Metall Trans B 22(6):875–888CrossRefGoogle Scholar
  35. 35.
    Tiaden J (1999) Phase field simulations of the peritectic solidification of Fe–C. J Cryst Growth 198:1275–1280CrossRefGoogle Scholar
  36. 36.
    Grill A, Brimacombe JK, Weinberg F (1976) Mathematical analysis of stresses in continuous casting of steel. Ironmak Steelmak 3(1):38–47Google Scholar
  37. 37.
    Chow C, Samarasekera IV, Walker BN, Lockhart G (2002) High speed continuous casting of steel billets: part 2: mould heat transfer and mould design. Ironmak Steelmak 29(1):61–69CrossRefGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Tarquínio Plynio Durães dos Anjos
    • 1
  • Paulo Vicente de Cassia Lima Pimenta
    • 1
  • Francisco Marcondes
    • 1
  1. 1.Department of Metallurgical Engineering and Material ScienceFederal University of Ceará Campus do PiciFortalezaBrazil

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