Temperature Calculation Using a Control Volume Technique

5 Temperature Calculation Using a Control Volume Technique 

The temperature increase calculation in Sections 7.7.1 and 7.7.2 was based on the viscosity using the temperature at the entry to the metering section. Because the temperature of the resin increases as it flows downstream, the shear viscosity continuously decreases. A better method to calculate the temperature of the resin in the channel is to divide the channel into many Az or Az increments, and then for each increment, perform an energy balance on each control volume [67]. A schematic of the control volume is shown in Fig. 7.36. The energy balance includes convection into and out of the volume, dissipation due to rotation and pressure flows, and energy conduction through the barrel wall and the root of the screw. This section will describe a control volume method for temperature calculation for both screw rotation and barrel rotation. 

The rate of work inputted by the rotating screw, energy conducted through the bar-rei wait, and energy conducted to the screw can be accounted for in each voiume. The energies dissipated tu here are based on the flow in a singie channei and a unit iength for the surface. The caicuiation is as foiiows for the voiume for screw rotation  

The energy dissipations for unit iength of Z, with units of J/(m-s) are as foiiows  

The integrations shown in Eqs. 7.99 and 7.100 are complex and are performed numerically. The heat transferred through the barrel wall over the channel for unit length Z(, is, and it is calculated using Eq. 7.102. A heat transfer expression 

---