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This paper presents a complete two-dimensional (2D) thermofluid model for predicting the neck-down shape in the fiber drawing process. This model uses the controlled draw tension to calculate the Neumann boundary condition at the furnace exit; thus, it does not require specifying the speed (or diameter) of the fiber as most previous studies did. The model presented here can be applied to optimization of the high-speed draw process with large-diameter preforms. In this study, the radiative transfer equation is directly solved for the radiation fluxes using the discrete ordinate method coupled with the solution of the free surface flow, which does not assume that the glass is optically thick and does not neglect the glass absorption at the short-wavelength band. The artificial compressibility method is used to solve the Navier-Stokes equations. A staggered-grid computation scheme that is shown to be efficient and robust was used to reduce the computation load in solving the complete 2D model. The neck-down profile of a large preform (9 cm dia) drawn at a relatively high speed of 25 m/s was experimentally measured. The measured profile well matches that derived numerically. Results also show that the free surface calculated using the Dirichlet boundary condition deviates considerably from the measured profile, particularly near the furnace exit where the actual diameter (and, hence, the speed of the glass) is essentially unknown. Although the difference between the numerical results obtained from the full and semi-2D models was small, this difference could be significant if the location at which the glass converges to 125 μm dia is of interest, especially when the preform has a large diameter drawn at a high speed.

This paper presents a method of modeling the radiative energy transfer that takes place during the transient of joining two concentric, semitransparent glass cylinders. Specifically, we predict the two-dimensional transient temperature and heat flux distributions to a ramp input which advances the cylinders into a furnace at high temperature. In this paper, we discretize the fully conservative form of two-dimensional Radiative Transfer Equation (RTE) in both curvilinear and cylindrical coordinate systems so that it can be used for arbitrary axisymmetric cylindrical geometry. We compute the transient temperature field using both the Discrete Ordinate Method (DOM) and the widely used Rosseland’s approximation. The comparison shows that Rosseland’s approximation fails badly near the gap inside the glass media and when the radiative heat flux is dominant at short wavelengths where the spectral absorption coefficient is relatively small. Most prior studies of optical fiber drawing processes at the melting point (generally used Myers’ two-step band model at room temperature) neglect the effects of the spectral absorption coefficient at short wavelengths λ<3μm. In this study, we suggest a modified band model that includes the glass absorption coefficient in the short-wavelength band. Our results show that although the spectral absorption coefficient at short wavelengths is relatively small, its effects on the temperature and heat flux are considerable.

Analytical solutions are derived for evaporating flow in open rectangular microchannels having a uniform depth and a width that decreases along the channel axis. The flow generally consists of two sequential domains, an entry domain where the meniscus is attached to the top corners of the channel followed by a recession domain where the meniscus retreats along the sidewalls toward the channel bottom. Analytical solutions applicable within each domain are matched at their interface. Results demonstrate that tapered channels provide substantially better cooling capacity than straight channels of rectangular or triangular cross section, particularly under opposing gravitational forces. A multiplicity of arbitrarily tapered channels can be microfabricated in metals using LIGA, a process involving electrodeposition into a lithographically patterned mold.