Zonal Method to Model Radiative Transport in an Optical Fiber Drawing Furnace

Precise modeling of radiative heat exchange between the furnace and the glass preform is a very important part of the modeling of the fiber drawing process in a high temperature furnace. Most earlier studies on this process have used the optically thick approximation, i.e., the radiative heat exchange is assumed to depend only on the preform surface temperature while the transmission, emission, and absorption within the preform are approximated as a diffusion process. The validity of this approximation in the modeling of the fiber drawing process is dubious since the diameter of the preform undergoes a drastic reduction during the drawing process. The objectives of this research are to use a more accurate approach—the zonal method—to replace the optically thick approximation for computing the radiative heat exchange between the furnace and the preform, and to determine if the optically thick approximation is valid for this process. In applying the zonal method, the preform surface is assumed to be diffuse to both transmission and reflection. An enclosure analysis is performed for the radiative exchange between the furnace and the outer surface of the preform and the zonal method is employed to consider the radiative exchange within the glass preform. The emissivity for the glass preform has been calculated based on the diffuse surface assumption and applied to the computation of radiative heat flux with the optically thick approximation for the purpose of comparison with the present work. The results obtained by the zonal method show that the radiative heat flux is strongly influenced by the radial temperature variation within the preform, while those obtained by the optically thick approximation do not show this effect, as expected. Comparisons of the results obtained by these two approaches reveal that the optically thick approximation predicts the radiative heat flux satisfactorily for a range of axial temperature variations, but only when the radial temperature variation within the preform is small. The diameter change in the neck-down region has almost no effect on the validity of the optically thick approximation.