Flow and heat transfer of a viscous melt in a supercooled capillary

• Published in: Chemie ingenieur technik Vol. 73; no. 7; pp. 843 - 848
• Main Author: Brod, H
• Format: Journal Article
• Language: German
• Published: 01-07-2001
• ISSN: 0009-286X

A mathematical model was developed to determine heat and mass transfer in a viscous polymer melt flowing under laminar flow conditions through a cylindrical capillary that is at a temperature lower than the solidification temperature of the melt. This analysis has practical significance to the extrusion and spinning of polymer melts into filaments. Assuming a Newtonian fluid and constant values of coefficients of viscosity, thermal conductivity, density, and heat capacity of the melt, the model predicts the position of the phase boundary and heat transfer within the flow channel. Dimensionless wall temperature gradient and relative thickness of the solidified melt in the tube were calculated as a function of dimensionless Fourier number based on solutions of the classical Graetz-Nusselt problem. Pressure changes in the melt flowing through the capillary are given as a function of the dimensionless Graetz number and dimensionless undercooling of the tube wall. A stability diagram was constructed from the model to delineate stable and unstable laminar flow regimes for the viscous melt flowing through an undercooled capillary tube.