A note on the steady Poiseuille flow of Carreau-Yasuda fluid

TL;DR

This paper investigates the steady Poiseuille flow of Carreau-Yasuda fluids in pipes, identifying conditions for classical and generalized solutions based on model parameters and pressure gradient.

Contribution

It provides a theoretical analysis distinguishing when classical versus generalized solutions exist for Carreau-Yasuda fluid flow in pipes.

Findings

Classical solutions exist for certain parameter values.

Generalized solutions occur under different conditions.

A necessary and sufficient condition for generalized solutions is derived.

Abstract

The steady Poiseuille flow of Carreau-Yasuda fluid in a pipe, caused by constant pressure gradient, is studied theoretically. It is proved that at some values of the viscosity model parameters, the problem has a classical solution, while at others - generalized solution. For the latter, a necessary and sufficient condition is found, which depends on the pressure gradient and Carreau-Yasuda model parameters.