Asymptotic equations for the terminal phase of glass fiber drawing and their analysis

In this article, we study mathematical modeling of thermal drawing of glass fibers. We give a derivation of the effective model from the generalized Oberbeck–Boussinesq equations with free boundary, using singular perturbation expansion. We generalize earlier approaches by taking the isochoric compressible model, with density depending on the temperature, and we handle correctly the viscosity, which changes over several orders of magnitude. For the obtained effective system of nonlinear differential equations, we prove the existence of a stationary solution for the boundary value problem. We impose only physically realistic assumptions on the data (viscosity taking large values with cooling). Finally we present numerical simulations with realistic data.