The Mathematical Institute, University of Oxford, Eprints Archive

Asymptotic solutions of glass temperature profiles during steady optical fibre drawing

Taroni, M. and Breward, C. J. W. and Cummings, L. J. and Griffiths, I. M. (2012) Asymptotic solutions of glass temperature profiles during steady optical fibre drawing. Journal of Engineering Mathematics . (Submitted)

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Abstract

In 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 the real industrial process, 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 into the dependencies of the solution on the parameters and the dominant heat-transport mechanism.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1640
Deposited By: Peter Hudston
Deposited On:05 Jan 2013 10:29
Last Modified:29 May 2015 19:20

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