Bauman Moscow State Technical University, Moscow, Russia

A. G. Zinyagin, Cand. Eng., Associate Prof., e-mail: ziniagin_ag@bmstu.ru
A. V. Muntin, Cand. Eng., Associate Prof., e-mail: muntin_av@bmstu.ru
A. P. Stepanov, Postgraduate Student, e-mail: Stepanov_ap@bmstu.ru
M. O. Kryuchkova, Senior Lecturer, e-mail: mariya.mironova@bmstu.ru
N. R. Borisenko, Postgraduate Student, e-mail: BorisenkoNikita17@yandex.ru

This article focuses on the numerical simulation of the cooling process of a pile of clad thick steel plates using the Finite Element Method (FEM). The main objective of the research is to predict the cooling time required for anti-flaking treatment and cooling of the stack to a temperature of 100 °C, after which sheet rolling can be unloaded from the slow cooling section. The relevance of the work stems from the fact that uneven cooling within the pile, caused by sheet flatness deviations, contact with the concrete floor, and other technological factors, directly affects the quality of the final product. During the study, a three-dimensional model based on the Finite Element Method was developed, which considers comprehensive heat transfer (conduction, convection, and radiation), variable thermophysical properties of the dissimilar layers of the bimetal (base layer K60 and cladding 08Kh18N10Т), as well as realistic production conditions: rolling rate, sequential pile formation, and surface roughness. The model was verified and adapted based on the results of a laboratory experiment, which allowed for refining the key heat transfer coefficients for steel-steel, steelconcrete, and steel-air contacts. As a result of simulating a series of industrial scenarios, analytical dependencies of the pile cooling time to 100 °C on the main technological parameters were obtained. It was established that the initial sheet temperature and the number of sheets in the pile (pile height) have the greatest influence, while the impact of the rolling rate is less significant. Based on the obtained data, empirical formulas describing these dependencies using power and logarithmic laws were derived. The practical significance of the work lies in providing a tool for the precise calculation of cooling process parameters, which enables process optimization, reduction of production time, and minimization of the risk of defects in clad steel plate.

1. Streisselberger A., Schwinn V., Hubo R. Microalloyed structural plate rolling heat treatment and applications. AG der Dillinger Huettenwerke 66748 Dillingen, Germany. 2003. Available at: https://niobium.tech/-/media/niobiumtech/attachments-biblioteca-tecnica/nt_microalloyed-structural-plate-rolling-heat-treatment.pdf (accessed: 29.01.2026)
2. Gorni A. A., da Silveira J. G. D. Accelerated cooling of steel plates: The time has come. J. ASTM Int. 2008. Vol. 5, Iss. 8. pp. 1–7.
3. Golovin S. V., Kravchenko A. G., Dremov V. P. Thermomechanical processing of high-strength thick sheet metal in the conditions of the metallurgical complex 5000 mill. Promyshlennoe i grazhdanskoe stroitelstvo. 2025. No. 12. pp. 50–55. DOI: 10.33622/0869-7019.2021.10.50-55
4. Huang Z., Shi Q., Chen F. et al. FEM simulation of the hydrogen diffusion in X80 pipeline steel during stacking for slow cooling. Acta Metall. Sin. (Engl. Lett.). 2014. Vol. 27. pp. 416–421. DOI: 10.1007/s40195-014-0073-z
5. Shen S.-D., Huang F.-X., Chen S.-H., Wang X.-H., Wang W.-J. Study on effect of stacking slowcooling before rolling on center-segregation of continuous casting slab. Iron & Steel. 2010. Vol. 45, Iss. 10. pp. 47–51.
6. Pyykkönen J. M., Martin D. C., Somani M. C., Mäntylä P. T. Thermal behaviour of steel plate during accelerated cooling. Materials Science Forum. 2010. Vols. 638–642. pp. 2706–2711. DOI: 10.4028/www.scientific.net/msf.638-642.2706
7. Jo H.-H., Kim K.-W., Park H., Moon J., Kim Y.-W., Shim H.-B., Lee C.-H. Estimation of cooling rate of high-strength thick plate steel during water quenching based on a dilatometric experiment. Materials. 2023. Vol. 16. 4792. DOI: 10.3390/ma16134792
8. Lee J., Samanta S., Steeper M. Review of accelerated cooling of steel plate. Ironmaking & Steelmaking: Processes, Products and Applications. 2015. Vol. 42, Iss. 4. pp. 268–273. DOI: 10.1080/1743281215Y.0000000010a
9. Ziniagin A. G. Use of machine learning methods for determination of the boundary conditions coefficients in a FEM task for the case of accelerated cooling of hot-rolled sheet metal. CIS Iron and Steel Review. 2023. Vol. 25. pp. 58–66
10. Zinyagin A. G., Muntin A. V., Stepanov A. P., Borisenko N. R. Study of the features of clad sheet deformation during hot rolling. Chernye Metally. 2023. No. 12. pp. 49–55.
11. Zinyagin A. G., Muntin A. V., Ilyinsky V. I., Nikitin G. S. Mathematical modeling of the process of accelerated cooling of a sheet on a 5000 mill. Problemy chernoy metallurgii i materialovedeniya. 2013. No. 1. pp. 9–15.
12. Spannar J., Sohlberg B. Modelling and identification of an air cooling process. Proceedings of the 1997 IEEE International Conference on Control Applications, Hartford, CT, USA, 1997. pp. 383–385. DOI: 10.1109/CCA.1997.627581
13. Speicher K., Steinboeck A., Kiefer T., Kugi A. Modeling thermal shocks and air cooling using the finite difference method. IFAC Proceedings Volumes. 2012. Vol. 45, Iss. 2. pp. 364–368. DOI: 10.3182/20120215-3-AT-3016.00064
14. Pietzsch R., Brzoza M., Kaymak Y., Specht E., Bertram A. Simulation of the Distortion of Long Steel Profiles During Cooling. ASME. J. Appl. Mech. 2007. Vol. 74, Iss. 3. pp. 427–437. DOI: 10.1115/1.2338050
15. Salganik V., Shmakov A., Pesin A., Pustovoytov D. Plate rolling modeling at mill 5000 of ojsc “magnitogorsk iron and steel” for analysis and optimization of temperature rates. AIP Conf. Proc. 15 June 2010. Vol. 1252, Iss. 1. pp. 602–607. DOI: 10.1063/1.3457609
16. Zinyagin A. G., Borisenko N. R., Stepanov A. P., Kryuchkova M. O. Development of measures to reduce longitudinal bending of thick clad and alloyed steel plates during hot rolling. CIS Iron and Steel Review. 2025. Vol. 29. pp. 56–60.
17. Zinyagin A. G., Muntin A. V., Tynchenko V. S. et al. Recurrent neural network (RNN)-based approach to predict mean flow stress in industrial rolling. Metals. 2024. Vol. 14, No. 12. 1329. DOI: 10.3390/met14121329
18. Zinyagin A. G., Borisenko N. R., Muntin A. V., Kruychkova M. O. Features of finite element modeling for hot rolling process of clad sheets and strips. CIS Iron and Steel Review. 2023. Vol. 26. pp. 51–57.
19. Jung Soo Ok, Hwan Suk Lim, Seonggon Kim, Yong Tae Kang. Heat transfer performance assessment for precise accelerated control cooling of the hot heavy clad plate. Case Studies in Thermal Engineering. 2023. Vol. 45. 102965. DOI: 10.1016/j.csite.2023.102965
20. Blazi V. Designer’s handbook. Construction physics. Moscow : Tekhnosfera, 2005. 536 p.
21. Neville A. M. Thermal properties of concrete. Moscow : Stroyizdat, 1972. 344 p.
22. Brimacombe J. K. Physical constants of some commercial steels at elevated temperatures. London, 1973. pp. 1–38.
23. Heung-Kyu Kim, Seong Hyeon Lee, Hyunjoo Choi. Evaluation of contact heat transfer coefficient and phase transformation during hot stamping of a hat-type Part. Materials. 2015. Vol. 8. pp. 2030–2042.
24. Isachenko V. P., Osipova V. A., Sukomel A. S. Thermal conductivity. Moscow : Energiya, 1975. 488 p.