Vectorial velocities

The scalar values for the vectorial velocities for the four polymer films that account for the heat transfer and dissipative melting may be calculated as follows ... 

It is now useful to examine the melting energy at the four solid interfaces for this new model and for the historical Tadmor model [8]. The dissipation data from the simulations are summarized in Table 6.1 for a PE resin with a viscosity of 880 Pa-s. Examination of the table points out that the vectorial velocities (V)) for Zones C and D are very different for the assumption of barrel and screw rotation, as presented previously and as shown in Table 6.1. Eor the historic model, all energy is dissipated in the Zone C melt film, and the cumulative energy for melting was calculated... 

Table 6.1 Calculated Vectorial Velocities for Zones C and D and the Melting Energies Developed in the Four Melt Films. The Simulations Were for a PE Resin with a Shear Viscosity of 880 Pa-s...

The analysis for Film D is developed in a similar manner except the vectorial velocity creating the dissipation is different and the film thickness calculation is different, as shown in Fig. A6.2(b). For Film D, the vectorial velocity gradient relative to the fixed barrel and rotating screw is defined as ... 

Notice that the dissipation term is four times as large as the one in Eq. A6.28. The barrel temperature is used here rather than the temperature of the trailing flight. In general, the temperature of the trailing flight is unknown. Derezinski [2] has shown, however, that the temperature of the flight is close to the local barrel temperature. The vectorial velocity in Film E is calculated as follows ... 

Horton (H9, K2), using a tapered tube, was able to match the velocity of fall of the drop with the velocity of the rising field and thereby observe the behavior of the system for an hour or more. Using a dark field trace photography technique, the semi-vectorial velocities were recorded. In every case the internal circulation was slowly damped out as the interface changed its character and became more contaminated. 

The vectorial velocities of both colliding particles before and after each collision event, denoted by v, V and v, V, respectively, satisfy the momentum and energy conservation law... 

The conservation laws in Eqs. (1) and (2), related to the elastic and exciting collisions, represent four scalar equations connecting the two vectorial velocities V, V before the collision event with the corresponding ones v, V after the event. 

The force Fp makes an angle 0 with the plane perpendicular to the screw axis see Fig. 7.10. The direction of force F is determined by the direction of the vectorial velocity difference between the barrel and the solid bed ... 

The vectorial velocity difference Av between the barrel velocity Vt, and the solid bed velocity v is ... 

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