On generalized Newtonian fluids in curved pipes

TL;DR

This paper investigates the flow of shear-dependent Newtonian fluids in curved pipes, establishing mathematical existence, uniqueness, and secondary flow characterization, and analyzing approximations by Dean-like equations.

Contribution

It provides new theoretical results on existence, uniqueness, and secondary flows for shear-dependent fluids in curved pipes, including approximation methods.

Findings

Proved existence and uniqueness of solutions.

Characterized secondary flows in curved pipes.

Analyzed approximation by Dean-like equations.

Abstract

This paper is concerned with steady, fully developed motion of a Navier-Stokes fluid with shear-dependent viscosity in a curved pipe under a given axial pressure gradient. We establish existence and uniqueness results, derive appropriate estimates and prove a characterization of the secondary flows. The approximation, with respect to the curvature ratio, of the full governing systems by some Dean-like equation is studied.