Velocity profiles, modeling melt

The factor /2 < 1 for b < 0 (T > 7o) that is, flow rate drops if the temperature of the dragging surface is higher than the stationary wall, and vice versa. Since the shear stress is constant across the gap, in the former case, and the viscosity drops as we approach the moving plate, and, therefore, the shear rate must increase (so that the product is constant), and the velocity profile becomes convex. This effect, as we will see in the melting model discussed later, strongly affects the melting rate. 

Fig. 9.32 A differential volume element perpendicular to the melt film-solid bed interface. Schematic view of temperature profile in the film and solid bed shown at right. Schematic views of velocity profiles (isothermal model) in the x and z directions are also shown.

Figure 12.33 gives velocity profiles for the PP/PS system, which were obtained with the aid of Eqs. 12.3-21 and 12.3-22, using volumetric flow rates and pressure gradients determined experimentally in a rectangular channel. Figure 12.34 gives plots of viscosity versus shear stress for the PP and PS employed. It is seen that the polymer melts obey a Power Law model for y > 10s 1. 

C.5 Velocity Profile for Flow in a Capillary. Although the Carreau model describes the viscosity behavior of polymer melts accurately, it is not possible to obtain analytical expressions for the velocity field for one-dimensional flows such as occur in a capillary. Obtain the velocity field for HOPE at 180 °C. (Use the Carreau model parameters in Table 2.2 by using the IMSL subroutine BVPFD, which is described in Appendix D.9 or BVP4C in MATLAB.)... 

One of the common problems associated with underwater pelletizers is the tendency of the die holes to freeze off. This results in nonuniform polymer melt flow, increased pressure drop, and irregular extrudate shape. A detailed engineering analysis of pelletizers is performed which accounts for the complex interaction between the fluid mechanics and heat transfer processes in a single die hole. The pelletizer model is solved numerically to obtain velocity, temperature, and pressure profiles. Effect of operating conditions, and polymer rheology on die performance is evaluated and discussed. 

It is possible to derive an expression for the pressnre profile in the x direction using a simple model. We assnme that the flow is steady, laminar, and isothermal the flnid is incompressible and Newtonian there is no slip at the walls gravity forces are neglected, and the polymer melt is uniformly distribnted on the rolls. With these assnmptions, there is only one component to the velocity, v dy), so the equations of continuity and motion, respectively, reduce to... 

Equations 9.3-22 and 9.3-26 are the basic equations of the melting model. We note that the solid-bed profile in both cases is a function of one dimensionless group ijj, which in physical terms expresses the ratio of the local rate of melting per unit solid-melt interface JX /X to the local solid mass flux into the interface Vszps, where ps is the local mean solid bed density. The solid-bed velocity at the beginning of melting is obtained from the mass-flow rate... 

Fig. 10.48 Numerical simulation results of nonisothermal flow of HDPE, Melt Flow Index MFI = 0.1 melt obeying the Carreau-Yagoda model for a typical FCM model wedge of e/h — 3 and =15. (a) Velocity (b) shear rate and (c) temperature profiles [Reprinted by permission from E. L. Canedo and L. N. Valsamis, Non Newtonian and Non-isothermal Flow between Non-parallel Plate - Applications to Mixer Design, SPE ANTEC Tech. Papers, 36, 164 (1990).]...

Figure 9 (a) Schematic representation of fountain flow, showing the velocity and shear rate profiles and the deformation of a cubic element of melt as it approaches the flow front, (b) Model for growth of the frozen layer in a mould cavity... 

The first step in determining the solid bed profile is to determine the temperature distribution in the melt. Referring back to Figure 8.15 we now develop the model. First, we locate a set of axes at the melt-solid interface at the trailing flight (right side of Fig. 8.15). Next, we make the following postulates for the velocity and temperature fields in the melt film ... 

In the study, the mathematical model of the polymer melt flows in the extrusion process of plastic profile with metal insert was developed and the complex melt rheological behavior was simulated based on the finite element method. The melt flow characteristic in the flow channel was analyzed. The variation of the melt pressure, velocity, viscosity and stress versus different metal insert moving rate was investigated. Some suggestions on its practical manufacturing control were concluded based on the simulation results. 

If the geometries of individual flow channels are modified in a profile die, this gives rise to a different transverse flow behavior and hence a different velocity distribution of the melt in the die. This paper puts forwards a means of aligning these transverse flows to the model version so that the velocity distribution of the melt in the main version is the same as that in the model version. 

Besides taking into accoiuit specific material properties, the developed model for a quasi-simultaneous welding process is capable for the first time to consider directly welding pressure, scan welding velocity and scan length to calculate temperature and melt displacement profiles. 

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