Correction factors for the drag and pressure flows of power-law fluids through rectangular ducts

There are many industrial examples of low Reynolds number non-Newtonian flows through rectangular ducts in polymer processing. They occur in all types of manufacturing processes in which raw polymeric materials are converted into products, ranging from screw extrusion to shaping operations in dies and molds. In addition, they are found in numerous rheological measurement systems. The literature provides various mathematical formulations for non-Newtonian flows through rectangular ducts, but-if not simplified further-their solution usually requires use of numerical techniques. Removing the need for these time-consuming techniques, we present novel analytical correction factors for the drag and pressure flows of power-law fluids in rectangular flow channels. We approximated numerical results for a fully developed flow under isothermal conditions using symbolic regression based on genetic programming. The correction factors can be applied to the analytical theory that describes the flow of power-law fluids between parallel plates to include effects of the side walls in the prediction of flow rate and viscous dissipation.

Melt Conveying in Single-Screw Extruders: Modeling and Simulation

Numerous analyses have modeled the flow of polymer melts in the melt-conveying zones of single-screw extruders. While initial studies mainly provided exact analytical results for combined drag and pressure flows of Newtonian fluids, more recently developed, numerical methods seek to deepen the understanding of more realistic flow situations that include shear-thinning and non-isothermal effects. With the advent of more powerful computers, considerable progress has been made in the modeling and simulation of polymer melt flows in single-screw extruders. This work reviews the historical developments from a methodological point of view, including (1) exact analytical, (2) numerical, and (3) approximate methods. Special attention is paid to the mathematical models used in each case, including both governing flow equations and boundary conditions. In addition, the literature on leakage flow and curved-channel systems is revisited.