Draining under gravity in steel galvanization.

Abstract

The problem of the coating of steel has been considered in several Mathematics in Industry study groups. In this process, after passing through a bath of molten alloy, steel sheeting is drawn upward to allow draining under gravity and stripping using an air knife, leaving a coating of desirable thickness. Here we discuss some aspects of the problem and in particular the gravity draining component. The problem is a very nice introduction to industrial modelling for students, but is also relevant for manufacturing. References Elsaadawy, E. A., Hanumanth, G. S., Balthazaar, A. K. S., McDermid, J. R., Hrymak, A. N. and Forbes, J.F. ``Coating weight model for the continuous hot-dip galvanizing process'', Metal. Mat. Trans. B, 38:413–424, 2007. doi:10.1007/s11663-007-9037-2 Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Roberts M. ``Coating Deformation in the jet stripping process'' in Proceedings of the 2009 Mathematics and Statistics in Industry Study Group, Eds. T. Marchant, M. Edwards, G. Mercer. Wollongong, Austealia, 2010. https://documents.uow.edu.au/content/groups/public/@web/@inf/@math/documents/doc/uow073330.pdf Hocking, G. C., Sweatman, W. L., Fitt, A. D., and Breward, C. ``Deformations arising during air-knife stripping in the galvanization of steel'', in Progress in Industrial Mathematics at ECMI 2010, Eds. M. Gunther, A. Bartel, M. Brunk, S. Schops, M. Striebel. Mathematics in Industry 17, pp. 311-317. Springer, Berlin Heidelberg, 2011. doi:10.1007/978-3-642-25100-9_36 Hocking, G. C., Lavalle, G., Novakovic, R., O'Kiely, D., Thomson, S., Mitchell, S. J., Herterich, R. ``Bananas–-defects in the jet stripping process''. Proceedings of the European Study Group with Industry in Mathematics and Statistics Research Collection. Rome Italy, 2016. https://researchrepository.ucd.ie/handle/10197/10215 Howison, S. D. and King, J. R. ``Explicit solutions to six free-boundary problems to fluid flow and diffusion''. IMA J. Appl. Math. 42:155–175, 1989. doi:10.1093/imamat/42.2.155 Hocking, G. C., Sweatman, W., Fitt, A. D. and Breward, C. ``Deformations during jet-stripping in the galvanizing process''. J. Eng. Math. Tuck Special Issue, 70:297–306, 2011. doi:10.1007/s10665-010-9394-8 Thornton, J. A. and Graff, H. F. ``An analytical description of the jet-finishing process for hot-dip metallic coatings on strip''. Metal. Mat. Trans. B, 7:607–618, 1976. doi:10.1007/BF02698594 Tuck, E. O. ``Continuous coating with gravity and jet stripping''. Phys. Fluids, 26(9):2352–2358, 1983. doi:10.1063/1.864438 Tuck, E. O., Bentwich, M., and van der Hoek, J. ``The free boundary problem for gravity-driven unidirectional viscous flows''. IMA J. Appl. Math. 30:191–208, 1983. doi:10.1093/imamat/30.2.191