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 pi p,z, the power-law exponent n, and the screw-pitch ratio t/Db. 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 power-law 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. POLYM. ENG. SCI., 58:2055-2070, 2018. (c) 2018 The Authors Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers