The thermodynamically consistent blend model of Dressler and Edwards [M. Dressler, 131 Edwards, Rheology of polymer blends with matrix-phase viscoelasticity and a narrow droplet size distribution, J. Non-Newtonian Fluid Mech. 120 (2004) 189-205] has been solved computationally to understand isothermal flow of polymer blends in the conveying zone of single screw extruders. Extending the method proposed by Dressler and Edwards [M. Dressler, B.J. Edwards, A method for calculating theological and morphological properties of constant-volume polymer blend models in inhomogeneous shear fields, J. Non-Newtonian Fluid Mech. 130 (2005) 77-95] to non-symmetric flow fields, the dynamic model has been solved for mixed Couette/Poiseuille flow as encountered in the conveying zone of single screw extruders. In the code, we consider both the mixing flow perpendicular to and the conveying flow parallel to the flights and we neglect flight edge effects. We show calculations for different model (e.g. blend component viscosity ratio) and flow geometry parameters (e.g. helix angle of the extruder screw) to understand qualitatively microstructure-rheology relationships for polymer blends in extrusion flows. Macroscopic flow characteristics such as the volumetric throughput, the residence time distribution function, and the non-Newtonian flow stresses are discussed along with microscopic characteristics of the blend such as oblate/prolate configurations of the droplets and break-up/coalescence rates. We discuss the results comparing with the Newtonian and power law fluid and in view of experimental evidence. (c) 2007 Elsevier B.V. All rights reserved.