A mathematical analysis of the stability of non- isothermal hollow fiber drawing

Constructing a mathematical model of non-isothermal drawing hollow fiber, with the technological parameters of the process and the properties of the workpiece is the main aim of the research. In order to achieve this, a non-isothermal process of drawing hollow fiber, which has form of system of nonlinear partial differential equations, is considered. A system describing the corresponding stationary flow has been compiled and solved. Linearization of the capillary drawing process in the vicinity of the found stationary state was performed. Then, using the separation variables method and discretization by finite differences, the analysis of linear stability was reduced to an eigenvalue problem.