Fundamental understanding of flow of suspensions is key in many different areas such as bioengineering, oil, food, pharmaceutical and cosmetic industries. Two important phenomena may occur in the flow of particle suspensions. The first is associated with the relaxation process of particles toward a rest state after the flow is stopped that leads to shear-sensitive viscosity. The second is associated with particle particle interaction that leads to shear-induced particle migration. The intensity of each of these effects is directly associated with particle size and imposed deformation rate. The available analyses are usually limited to one of these phenomena. A common approach is to consider that the suspension viscosity varies with shear rate, using a viscosity function to describe this dependency, and that the particle concentration is uniform throughout the flow. Most of the studies that consider shear-induced particle migration assume that the viscosity varies only with the local particle concentration and is not a function of shear rate. The range of validity and accuracy of these two approaches is not well understood. In this work, we analyze the fully-developed flow of particle suspensions in a tube using different flow models to evaluate the effect of both particle migration and shear dependent viscosity. The results show that, at certain conditions, accurate predictions on the flow rate-pressure gradient relation can only be made by considering both phenomena in a fully coupled, non-linear flow model. (C) 2016 Elsevier B.V. All rights reserved.