In this work we present a study on flows of Newtonian and Non-Newtonian fluids, carried out both analytically and numerically. Industrial applications of these flows are found in classical industries such as in polymer processing (for instance in extrusion) and in more modern applications as in lab-on-chip devices.

For the numerical solution of the governing equations (continuity, momentum and a constitutive equation that relates the stress to the velocity fields) we used the Finite Volume Method together with a projection method for coupling the velocity and pressure fields.

In this presentation the discretization approaches and the different methods used to obtain the numerical solution will be described and discussed. Moreover, several case studies related to the design of extruded profile forming tools and the impact of the boundary conditions on their performance, will be presented.