5.2 Field synergy analysis

In order to verify the field synergy effect, we calculated the mean field synergy angle between temperature gradient and velocity fields and the Nusselt number at different screw speeds for these six screws as shown in Figure 7. It can be seen that the Nusselt number increases with screw speed, which is a well-known fact. Results also indicated that conventional screw E without torsion elements has the largest mean field synergy angle and smallest Nusselt number, while screw F without screw elements has the smallest mean field synergy angle and largest Nusselt number, which means the smaller the field synergy angle, the larger the Nusselt number. However, there are little difference of values in field synergy angle and Nusselt number for the screws A, B, C and D. This is because all these four screws have the same six torsion elements, which bring about almost the same influence on the variations of field synergy angle, that is, the arrangement of torsion elements in the screw has little effect on the field synergy angle. Therefore, it can be inferred that the screws equipped with torsion elements show better convective heat transfer capacity compared with the conventional screw, which then bring about a good melt temperature uniformity.

In addition, Figure 8 shows the local field synergy angle and the local heat transfer coefficient at different cross sections for screw A. Results also indicated that the local regions with torsion elements have larger heat transfer coefficients and smaller field synergy angles than the local regions with screw elements. Besides, the local convective heat transfer was found to be inversely proportional to the local field synergy angle between velocity and temperature gradient.

The contours of the local field synergy angle at different positions further show that most of the local synergy angle distributions at the cross sections of torsion elements alternate between larger and smaller synergy angles, while those at the cross sections of screw elements are close to 90.0°.

Figure 9 shows the dependence of the Nusselt number on the field synergy angle for various screw speeds and shows that the Nusselt number increases with

decreasing field synergy angle. It can be inferred that the Nusselt number is inversely interrelated with the synergy angle β. When the confidence level is 95%, its value is limited to a relatively narrow confidence band. Furthermore, the Pearson correlation coefficient is about 0.7, which indicates a strong negative correlation. These results demonstrate that the coupling relationship between temperature gradient and velocity fields has a significant effect on the convective heat transfer of

The dependence of the Nusselt number on the field synergy angle for various screw speeds. The inset is the

A plot of the local field synergy angle versus the local heat transfer coefficient (left) and the local field synergy

Multi-Field Synergy Process for Polymer Plasticization: A Novel Design Concept for Screw…

DOI: http://dx.doi.org/10.5772/intechopen.89616

angle contours at different cross sections (right) for screw A at a screw speed of 80 r/min.

Accordingly, the field synergy principle is able to explain the enhancement of

the polymer itself in a polymer plasticization process.

Figure 8.

Figure 9.

27

Pearson correlation coefficient.

heat transfer brought about by the torsion elements.

Figure 7. A plot of the mean field synergy angle (left) and Nusselt number (right) versus screw speed for various screws.

Multi-Field Synergy Process for Polymer Plasticization: A Novel Design Concept for Screw… DOI: http://dx.doi.org/10.5772/intechopen.89616

#### Figure 8.

or after the torsion element. It can be concluded that the torsion element can achieve more uniform temperature distribution than the screw element.

In order to verify the field synergy effect, we calculated the mean field synergy angle between temperature gradient and velocity fields and the Nusselt number at different screw speeds for these six screws as shown in Figure 7. It can be seen that the Nusselt number increases with screw speed, which is a well-known fact. Results also indicated that conventional screw E without torsion elements has the largest mean field synergy angle and smallest Nusselt number, while screw F without screw elements has the smallest mean field synergy angle and largest Nusselt number, which means the smaller the field synergy angle, the larger the Nusselt number. However, there are little difference of values in field synergy angle and Nusselt number for the screws A, B, C and D. This is because all these four screws have the same six torsion elements, which bring about almost the same influence on the variations of field synergy angle, that is, the arrangement of torsion elements in the screw has little effect on the field synergy angle. Therefore, it can be inferred that the screws equipped with torsion elements show better convective heat transfer capacity compared with the conventional screw, which then bring about a good

In addition, Figure 8 shows the local field synergy angle and the local heat transfer coefficient at different cross sections for screw A. Results also indicated that the local regions with torsion elements have larger heat transfer coefficients and smaller field synergy angles than the local regions with screw elements. Besides, the local convective heat transfer was found to be inversely proportional to the local

The contours of the local field synergy angle at different positions further show that most of the local synergy angle distributions at the cross sections of torsion elements alternate between larger and smaller synergy angles, while those at the

Figure 9 shows the dependence of the Nusselt number on the field synergy angle for various screw speeds and shows that the Nusselt number increases with

A plot of the mean field synergy angle (left) and Nusselt number (right) versus screw speed for various screws.

field synergy angle between velocity and temperature gradient.

cross sections of screw elements are close to 90.0°.

5.2 Field synergy analysis

Thermosoftening Plastics

melt temperature uniformity.

Figure 7.

26

A plot of the local field synergy angle versus the local heat transfer coefficient (left) and the local field synergy angle contours at different cross sections (right) for screw A at a screw speed of 80 r/min.

#### Figure 9.

The dependence of the Nusselt number on the field synergy angle for various screw speeds. The inset is the Pearson correlation coefficient.

decreasing field synergy angle. It can be inferred that the Nusselt number is inversely interrelated with the synergy angle β. When the confidence level is 95%, its value is limited to a relatively narrow confidence band. Furthermore, the Pearson correlation coefficient is about 0.7, which indicates a strong negative correlation. These results demonstrate that the coupling relationship between temperature gradient and velocity fields has a significant effect on the convective heat transfer of the polymer itself in a polymer plasticization process.

Accordingly, the field synergy principle is able to explain the enhancement of heat transfer brought about by the torsion elements.

Figure 10.

The streamline contours in screws A, B, and E at a screw speed of 40 r/min in the axial direction (a) and the cross section of the torsion element (b).
