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Generally, numerical methods are required to model the non-Newtonian flow of polymer melts in single-screw extruders. Existing approximation equations for modeling the throughput–pressure relationship and viscous dissipation are limited in their scope of application, particularly when it comes to special screw designs. Maximum dimensionless throughputs of ΠV < 2.0, implying minimum dimensionless pressure gradients Πp,z ≥ -0.5 for low power-law exponents are captured. We present analytical approximation models for predicting the pumping capability and viscous dissipation of metering channels for an extended range of influencing parameters (Πp,z ≥ -1.0, and t/Db ≤ 2.4) required to model wave- and energy-transfer screws. We first rewrote the governing equations in dimensionless form, identifying three independent influencing parameters: (i) the dimensionless down-channel pressure gradient Πp,z, (ii) the power-law exponent n, and (iii) the screw-pitch ratio tDb. We then carried out a parametric design study covering an extended range of the dimensionless influencing parameters. Based on this data set, we developed regression models for predicting the dimensionless throughput-pressure relationship and the viscous dissipation. Finally, the accuracy of all three models was proven using an independent data set for evaluation. We demonstrate that our approach provides excellent approximation. Our models allow fast, stable, and accurate prediction of both throughput-pressure behavior and viscous dissipation.

Modeling the non-Newtonian flow of polymer melts in single-screw extrusion generally requires numerical methods. This study analyzes the viscous dissipation of the melt-conveying zone, which is mainly responsible for the axial melt temperature increase, in single-screw extruders for both one-and two-dimensional stationary, fully developed flows of a power-law fluid. Rewriting the flow equations and applying the theory of similarity revealed three independent parameters that influence the physics of the fluid flow: the dimensionless pressure gradient P p;z , the power-law exponent n, and the screw-pitch ratio t=D b . Based on these parameters, we carried out a comprehensive numerical parametric study evaluating viscous dissipation and flow rate. Here, we present four heuristic models that predict the viscous dissipation of a powerlaw fluid in the melt-conveying zone of single-screw extruders. For one-dimensional and two-dimensional flows, we developed models for both a given pressure gradient and a given throughput. The approximation equations obtained allow fast and stable prediction without the need for numerical simulations of viscous dissipation. The accuracy of the heuristic models developed was validated in an error analysis, which showed that our approaches provide excellent approximations of the numerical results.