A finite element analysis of the upper jet region of a fiber drawing flow field

A heat transfer model is developed to analyze the upper jet region of a fiber drawing flow field. This region is characterized by fully two diminsional fields and a large change in the radius of the jet. Because of these and other analytic complexities such as viscous dissipation, temperature-dependent viscosity, the determination of the free surface shape of the jet, gravity, inertia, and surface tension forces; the upper jet region is analyzed by the finite element method. A boundary layer theory is presented which accounts for the stretching jet surface. The Karman-Pohlhausen momentum-integral technique is used with an assumed velocity profile motivated by the shearing flow between two concentric cylinders in relative axial motion. A stretching jet surface imposes on the boundary layer a development which is distinct from that which is normally encountered on a constant radius cylinder. Reynolds' analogy is assumed for the calculation of convective heat transfer from the jet to an air boundary layer.