Single Screw Extrusion—Isothermal Flow Problems

1 SINGLE SCREW EXTRUSION-ISOTHERMAL FLOW PROBLEMS 

Determining the effect of viscous dissipation in the metering section of a single screw extruder. Consider a 60 mm diameter extruder with a4 mm channel depth and a screw speed of 60 rpm. The melt used in this extrusion system is a polycarbonate with a viscosity of 100 Pa-s, a thermal conductivity of 0.2 W/m/K and a heater temperature of 300°C. To assess the effect of viscous heating we can choose a temperature difference, AT of 30K. This simply means that the heater temperature is 30K above the melting temperature of the polymer. For this system, the Brinkman number becomes 

This can be easily checked by assuming that the flow inside this section of the screw can be modeled using a simple shear flow, and that most of the conduction occurs through the channel thickness direction. For such a case, the energy equation in that direction, say the -direction, reduces to 

If we integrate eqn. (6.3) two times and use a boundary condition of To the screw and barrel surfaces, we get 

Setting y =0.002 m, which is located in the middle of the channel and using the above data, we get a temperature of 306.6°C, a 6.6 K temperature rise. Although there is a measurable temperature rise in this system, it is not significant enough to warrant a non-isothermal analysis. 

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