scholarly journals Non-isothermal process of viscoelastic polymer fi lm casting

2019 ◽  
pp. 27-29 ◽  
Author(s):  
A. V. Вaranov
Keyword(s):  
Surface Tension ◽  
Steady State ◽  
Polymer Melt ◽  
Maxwell Model ◽  
Air Cooling ◽  
Isothermal Process ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Uniaxial Stretching ◽  
Dependent Viscosity

The steady-state non-isothermal process of viscoelastic fl at polymer fi lm casting is considered. The polymer melt is extruded through a fl at die, subjected to uniaxial stretching and at the same time air cooling, and then fi nally cooled down on a chill roll. It is assumed that the fi lm is wide enough, the distance between the extruder die and the cooling roller is minimal to such an extent that it is possible to neglect change of width of a fi lm in the course of longitudinal stretching. It is also believed that the forces of gravity, inertia and surface tension can be ignored. From a rheological standpoint, polymer melt is the viscoelastic fl uid. The upper-convective Maxwell model with temperature-dependent viscosity is used. The problem is solved by a numerical method of fi nite diff erences.

A numerical study of solidification and viscous dissipation effects on polymer melt flow in plane channels

2013 ◽  
Vol 33 (2) ◽  
pp. 95-110
Author(s):  
Mustafa Tutar ◽  
Ali Karakus
Keyword(s):  
Shear Rate ◽  
Phase Change ◽  
Viscous Dissipation ◽  
Polymer Melt ◽  
Viscous Heating ◽  
Transient Phase ◽  
Melt Flow ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity

Abstract The combined effects of solidification and viscous dissipation on the hydrodynamic and thermal behavior of polymer melt flow during the injection process in a straight plane channel of constant cross section are numerically studied by considering the shear-rate and temperature-dependent viscosity and transient-phase change behavior. A numerical finite volume method, in conjunction with a modified form of the Cross constitutive equation to account for shear rate, temperature-dependent viscosity changes and a slightly modified form of the method proposed by Voller and Prakash to account for solidification of the liquid phase, is used and a validation with an analytical solution is presented for viscous heating effects. The hydrodynamic and solidified layers growth under the influence of a transient phase-change process and viscous dissipation, are analyzed for a commercial polymer melt flow, polypropylene (PP) for different parametric conditions namely, inflow velocity, polymer injection (inflow) temperature, the channel wall temperature, and the channel height. The results demonstrate that the proposed numerical formulations, including conjugate effects of viscous heating and transient-solidification on the present thermal transport process, can provide an accurate and realistic representation of polymer melt flow behavior during the injection molding process in plane channels with less simplifying assumptions.

New correlation for the temperature-dependent viscosity for saturated liquids

2016 ◽  
Vol 30 (32n33) ◽  
pp. 1650399 ◽  
Author(s):  
Jianxiang Tian ◽  
Laibin Zhang
Keyword(s):  
Surface Tension ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Average Deviation ◽  
New Correlation ◽  
Multiple Parameter ◽  
The One ◽  
Dependent Viscosity ◽  
Better Than ◽  
Triple Point Temperature

Based on the recent progress on both the temperature dependence of surface tension [H. L. Yi, J. X. Tian, A. Mulero and I. Cachading, J. Therm. Anal. Calorim. 126 (2016) 1603, and the correlation between surface tension and viscosity of liquids [J. X. Tian and A. Mulero, Ind. Eng. Chem. Res. 53 (2014) 9499], we derived a new multiple parameter correlation to describe the temperature-dependent viscosity of liquids. This correlation is verified by comparing with data from NIST Webbook for 35 saturated liquids including refrigerants, hydrocarbons and others, in a wide temperature range from the triple point temperature to the one very near to the critical temperature. Results show that this correlation predicts the NIST data with high accuracy with absolute average deviation (AAD) less than 1% for 21 liquids and more than 3% for only four liquids, and is clearly better than the popularly used Vogel–Fulcher–Tamman (VFT) correlation.

Extension of a viscous thread with temperature-dependent viscosity and surface tension

2016 ◽  
Vol 800 ◽  
pp. 720-752 ◽  
Author(s):  
Dongdong He ◽  
Jonathan J. Wylie ◽  
Huaxiong Huang ◽  
Robert M. Miura
Keyword(s):  
Surface Tension ◽  
Reynolds Number ◽  
Temperature Profile ◽  
Solid Wall ◽  
Analytic Solutions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Initial Shape ◽  
Vertically Aligned ◽  
Dependent Viscosity

We consider the evolution of a long and thin vertically aligned axisymmetric viscous thread that is composed of an incompressible fluid. The thread is attached to a solid wall at its upper end, experiences gravity and is pulled at its lower end by a fixed force. As the thread evolves, it experiences either heating or cooling by its environment. The heating affects the evolution of the thread because both the viscosity and surface tension of the thread are assumed to be functions of the temperature. We develop a framework that can deal with threads that have arbitrary initial shape, are non-uniformly preheated and experience spatially non-uniform heating or cooling from the environment during the pulling process. When inertia is completely neglected and the temperature of the environment is spatially uniform, we obtain analytic solutions for an arbitrary initial shape and temperature profile. In addition, we determine the criteria for whether the cross-section of a given fluid element will ever become zero and hence determine the minimum stretching force that is required for pinching. We further show that the dynamics can be quite subtle and leads to surprising behaviour, such as non-monotonic behaviour in time and space. We also consider the effects of non-zero Reynolds number. If the temperature of the environment is spatially uniform, we show that the dynamics is subtly influenced by inertia and that the location at which the thread will pinch is selected by a competition between three distinct mechanisms. In particular, for a thread with initially uniform radius and a spatially uniform environment but with a non-uniform initial temperature profile, pinching can occur either at the hottest point, at the points near large thermal gradients or at the pulled end, depending on the Reynolds number. Finally, we show that similar results can be obtained for a thread with initially uniform radius and uniform temperature profile but exposed to a spatially non-uniform environment.

scholarly journals Non-Isothermal Creeping Flows in a Pipeline Network: Existence Results

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1300
Author(s):  
Evgenii S. Baranovskii ◽  
Vyacheslav V. Provotorov ◽  
Mikhail A. Artemov ◽  
Alexey P. Zhabko
Keyword(s):  
Nonlinear Boundary ◽  
Galerkin Approximation ◽  
Large Data ◽  
Temperature Dependent ◽  
Weak Formulation ◽  
Temperature Dependent Viscosity ◽  
Pipeline Network ◽  
Flux Boundary Conditions ◽  
Creeping Flows ◽  
Dependent Viscosity

This paper deals with a 3D mathematical model for the non-isothermal steady-state flow of an incompressible fluid with temperature-dependent viscosity in a pipeline network. Using the pressure and heat flux boundary conditions, as well as the conjugation conditions to satisfy the mass balance in interior junctions of the network, we propose the weak formulation of the nonlinear boundary value problem that arises in the framework of this model. The main result of our work is an existence theorem (in the class of weak solutions) for large data. The proof of this theorem is based on a combination of the Galerkin approximation scheme with one result from the field of topological degrees for odd mappings defined on symmetric domains.

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