Asymptotic solutions of glass temperature profiles during steady optical fibre drawing
KAUST Grant NumberKUK-C1-013-04
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AbstractIn this paper we derive realistic simplified models for the high-speed drawing of glass optical fibres via the downdraw method that capture the fluid dynamics and heat transport in the fibre via conduction, convection and radiative heating. We exploit the small aspect ratio of the fibre and the relative orders of magnitude of the dimensionless parameters that characterize the heat transfer to reduce the problem to one- or two-dimensional systems via asymptotic analysis. The resulting equations may be readily solved numerically and in many cases admit exact analytic solutions. The systematic asymptotic breakdown presented is used to elucidate the relative importance of furnace temperature profile, convection, surface radiation and conduction in each portion of the furnace and the role of each in controlling the glass temperature. The models derived predict many of the qualitative features observed in real industrial processes, such as the glass temperature profile within the furnace and the sharp transition in fibre thickness. The models thus offer a desirable route to quick scenario testing, providing valuable practical information about the dependencies of the solution on the parameters and the dominant heat-transport mechanism. © 2013 Springer Science+Business Media Dordrecht.
CitationTaroni M, Breward CJW, Cummings LJ, Griffiths IM (2013) Asymptotic solutions of glass temperature profiles during steady optical fibre drawing. J Eng Math 80: 1–20. Available: http://dx.doi.org/10.1007/s10665-013-9623-z.
SponsorsThis paper was conceived as an extension to a problem considered at the 27th Annual Workshop on Mathematical Problems in Industry held at the New Jersey Institute of Technology in June 2011, with funding from the National Science Foundation. We would like to thank A. Filippov from Corning Inc., who presented the problem at the workshop and gave us invaluable insight into the practical issues involved. We would also like to thank the other participants who worked on different aspects of the problem: R. Beckham, M. Gratton, M. Kanoria, K. Kilgore, V. Lapin, T-S. Lin, M. Ma, H. Nganguia, J. Pohlmeyer, H. Potter, D. Schwendeman, S. K. Wilson, and H. Yaple. Finally, the authors note that this publication was based on work supported in part by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).