Can anyone suggest me references for Carreau-Yasuda model for validation of fully developed Non-Newtonian flow inside a 3D Pipe ?

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Виталий Валерьевич Леваничев

I can only offer my work on the study of the velocity profile, the analysis of non-Newtonian fluid flow, using different models the full rheological curve.

Antoine Briard

Maybe it's a bit far from what you're looking for, but here is a paper about Carreau fluids, but in a 2D cell. Maybe you will nevertheless find some information about the velocity profile: the influence of varying the rheology constants of the model is studied.