The healing, drawing and cooling of fused silica have a great impact on the overall quality of the fiber. Thus, a clear understanding of the underlying physics is crucial. The present study seeks to evaluate the impact of simplifying assumptions in the treatment of the transport equations and the thermal conditions, as well as to evaluate the feasibility of adapting simpler models. The results showed a localization of the vorticity and viscous dissipation, and confirmed the existence of temperature and velocity gradients. The results also showed the necking shape, heat transfer coefficient and furnace temperature profiles to have a decisive impact on the overall solution. In addition, the approximation of setting the vorticity to zero was found to be a feasible alternative.