Temperature and Velocity Profiles in Drag Flow of a Temperature Dependent Power Law Fluid

Abstract

Abstract This paper analyzes non-isothermal drag flow between parallel plates. First, non-isothermal drag flow is considered of a Newtonian fluid with a non-zero pressure gradient, assuming viscous dissipation is negligible. Second, non-isothermal drag flow is considered of a power law fluid with zero pressure gradient, again assuming viscous dissipation is negligible. Finally, pure drag flow of a temperature dependent power law fluid is analyzed, including the effect of viscous dissipation. When the temperature of the stationary plate is increased, the flow rate increases. Applying this analysis to screw extrusion, this means that increasing the screw temperature relative to the barrel temperature will increase the flow rate. Also, the temperature sensitivity of the flow rate reduces with increasing screw temperature and with increasing power law index. This points to useful benefits of screw heating. With shear thinning fluids increased channel depth raises the stock temperatures, even though the shear rates in the fluid will be reduced. The increased temperatures are due to longer heat transfer distances; the viscous heat generated is less easily conducted away to the walls. At high values of the Brinkman number, the heat flux at the lower plate reduces when the upper plate temperature increases, while at low Brinkman numbers the opposite is true. This is important in the analysis of melting in extruders. It indicates that while high barrel temperatures in the melting zone may be beneficial at low screw speeds, it can be detrimental at high screw speeds. At high screw speeds, therefore, lower barrel temperatures may be more appropriate to obtain efficient melting.