Example Calculation of Energy Dissipation

In order to show the difference between screw and barrel rotation, a simple energy dissipation example is provided here. A complete analysis of energy dissipation will be presented in Section 7.7. For this example, a 50.8 mm diameter screw is rotated at a speed of 50 rpm and with a pressure gradient of zero, producing a rate of 6.8 cmys. The geometric data and physical property data are provided in Table 7.4. 

Evaluating the process aty = 0.5//, one obtains for the Lagrangian frame or barrel rotation the dissipation rate  

the temperature increase for the process is calculated via an energy balance w t, 

Evaluating the dissipation rate for the Eulerian or screw rotation  

This analysis indicates that screw and barrel rotation should have different temperature increases even though they have the same rate predicted for the same rotation rate. In the following section the predictions will be checked experimentally. 

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