Polymer Melt Flow in Plane Channels: Effects of the Viscous Dissipation and Axial Heat Conduction

Abstract

The plastic transforming industry has shown considerable growth in the last years. In this context, commercial simulators have been developed, some of which combine simplified mathematical models with rheological properties of commercial polymers. In spite of the successes, these approximations are not able to capture important details of the flow behavior. The present work addresses some aspects of the polymer melt flow in plane channels using a more elaborate mathematical formulation based on the full momentum and energy conservation laws. The physical equations are discretized using finite differences based on a collocated mesh and second-order spatial accuracy formulas. Solutions featuring the development of hydrodynamic and thermal boundary layers are presented for a commercial polymer.

Polymer melt flow in plane channels: Hydrodynamic and thermal boundary layers

“…The hydrodynamic and thermal problems are coupled and the flow solutions exhibit strong nonlinearity, especially through a shear-rate and temperature dependent viscosity. The recent literature [13][14][15] reflects the ongoing interest of the scientific community in further understanding the physics of such problems. The present paper is particularly concerned with the effect of the inlet velocity upon the development of the thermal and hydrodynamic boundary layers.…”

“…Further discussions on the phenomena associated with polymer melt flow in plane channels, including the axial heat conduction, viscous heating effect and Nusselt numbers, can be found in Ref. [15].…”

A fully implicit finite difference scheme for velocity and temperature coupled solutions of polymer melt flow

“…Koh et al [7], using the generalized Newtonian approach in conjunction with the finite volume method, focused their attention on the effect of different viscosity descriptions on temperature and velocity distributions. Jambal et al [8], using the power law constitutive model, and Zdanski and Vaz Jr [9], based on the Cross equation, addressed the effects of the viscous dissipation and axial heat conduction of polymer melt flow in planar channels. In this example, the inlet velocity is U 0 = 3 cm/s, and the inlet and wall temperatures are T 0 = T w = 423 K. The present simulation uses a Cartesian mesh with 41 nodes on the cross-section and 1501 nodes along the channel length, L = 375h.…”

“…The simulation shows that the fully developed velocity profile is virtually reached at x/ h = 2.5, whereas the temperature requires a channel length greater than 350h to achieve a fully developed profile. The reader is referred to Reference [9] for further discussions on the physics of the problem.…”

Non-isothermal polymer melt flow in sudden expansions

“…The numerical scheme is based on techniques originally conceived to solve Newtonian flows [8]. The capability of the computational scheme to handle non-Newtonian flows inside plane channels, as well as sudden expansions, has been previously demonstrated in Vaz Jr. and Zdanski [9] and Zdanski and Vaz Jr. [10,11]. These results indicated strong dependence of flow parameters on temperature.…”