Non-adiabatic elongational flows of viscoelastic melts
Elongational flows of viscoelastic melts are frequently encountered in manufacturing processes in the textile industry. The most common stretching flow is melt-spinning. In this process, a polymeric melt is withdrawn from a reservoir, axially stretched, and simultaneously cooled down until the melt freezes. This paper addresses the fundamental question of existence of solutions for the system of quasilinear hyperbolic equations governing the melt-spinning process of a Giesekus fluid and a Phan-Thien-Tanner fluid. The problem is originally posed as a free boundary problem. It will be shown that the free boundary problem can be reformulated as an equivalent boundary-initial value problem for which we prove the (local in time) existence of classical solutions.
Zeitschrift fur Angewandte Mathematik und Physik
Hagen, T., & Renardy, M. (2000). Non-adiabatic elongational flows of viscoelastic melts. Zeitschrift fur Angewandte Mathematik und Physik, 51 (6), 845-866. https://doi.org/10.1007/PL00001526