Non-Isothermal Flow of Molten Glass: Mathematical Challenges and Industrial Questions.

With specific reference to the process of glass fibers drawing we review the models proposed to describe the various stages of the flow of molten glass from the furnace to the winding spool: the slow flow in the die, the jet formation under rapid cooling, the terminal fiber profile. In the course of our exposition we will present a general model for non-isothermal flows of mechanically incompressible but thermally expansible fluids (the basic model here assumed for glass), and the Oberbeck–Boussinesq limit is discussed. Both the modelling and the mathematical aspects will be illustrated in detail. An appendix is devoted to the question of stability analysis. [ABSTRACT FROM AUTHOR]