# Heat Transfer During Annealing of Steel Coils

• Winston L. Sweatman
• Steven I. Barry
• Mark McGuinness
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 17)

## Abstract

Steel becomes brittle during the cold rolling process which is used to produce sheet metal. Heat treatment (annealing) is required to release stresses and reform the crystalline structure. The 2008 Mathematics-and Statistics-in- Industry Study Group in Wollongong (MISG08) modelled the approach used by New Zealand Steel for which steel coils are heated in a batch annealing furnace. Determining the temperature within each coil is complicated by height-dependent gaps within the coils. Deciding on suitable boundary conditions for the outside of the coils provides a further challenge. This is explored with two alternative models. Having made reasonable assumptions, a linear model is found to be sufficient for modelling the heating process and allows the cold point in the steel coil to be established.

## Keywords

Heat Transfer Suitable Boundary Condition Steel Coil Cold Rolling Process Coil Heat
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
McGuinness, M., Sweatman, W.L., Baowan, D., Barry, S.I.: Annealing Steel Coils. In: Merchant, T., Edwards, M., Mercer, G. (eds.) Proceedings of the 2008 Mathematics and Statistics in Industry Study Group, pp. 61–80. University of Wollongong, Australia (2009)Google Scholar
2. 2.
Hocking, G.C., Sweatman, W.L., Fitt, A.D., Breward, C.: Deformations during jet-stripping in the galvanizing process. J. Eng. Math. 70, 297–306 (2011), doi: 10.1007/s10665-010-9394-8
3. 3.
Landman, K., McGuinness, M.: Mean Action Time for Diffusive Processes. J. Appl. Math. Decis. Sci. 4(2), 125–141 (2000)
4. 4.
Stikker, U.O.: Numerical simulation of the coil annealing process. In: Mathematical Models in Metallurgical Process Development, Iron and Steel Institute, Special Report, 123, pp. 104–113 (1970)Google Scholar
5. 5.
Willms, A.R.: An exact solution of Stikker’s nonlinear heat equation. SIAM J. Appl. Math. 55(4), 1059–1073 (1995)
6. 6.
Sridhar, M.R., Yovanovicht, M.M.: Review of elastic and plastic contact conductance models: comparison with experiment. J. Thermophys. Heat Trans. 8, 633–640 (1994)
7. 7.
Zuo, Y., Wu, W., Zhang, X., Lin, L., Xiang, S., Liu, T., Niu, L., Huang, X.: A study of heat transfer in high-performance hydrogen Bell-type annealing furnaces. Heat Tran. Asian Res. 30(8), 615–623 (2001)
8. 8.
Zhang, X., Yu, F., Wu, W., Zuo, Y.: Application of radial effective thermal conductivity for heat transfer model of steel coils in HPH furnace Int. J. Thermophys. 24(5), 1395–1405 (2003)
9. 9.
Hickson, R., Barry, S., Mercer, G.: Exact and numerical solutions for effective diffusivity and time lag through multiple layers. ANZIAM J. (E) 50, C682–C695 (2009)Google Scholar
10. 10.
Budak, B.M., Samarskii, A.A., Tikhonov, A.N.: A collection of problems in mathematical physics. Dover, New York (1964)Google Scholar

## Authors and Affiliations

• Winston L. Sweatman
• 1
• Steven I. Barry
• 2
• Mark McGuinness
• 3
1. 1.Massey UniversityAucklandNew Zealand
2. 2.Australian National UniversityCanberraAustralia
3. 3.Victoria University of WellingtonWellingtonNew Zealand