Full perturbation solution for the flow in a rotated torus

TL;DR

This paper develops a perturbation solution for pressure-driven flow in a rotating torus, comparing it with simplified models and analyzing flow features at low Reynolds numbers.

Contribution

It introduces a comprehensive perturbation approach for flow in a rotating torus, extending previous simplified models and defining convergence conditions across parameters.

Findings

Solution reliable at low Reynolds numbers

Flow exhibits unique patterns and hydrodynamic features

Convergence conditions established for all parameters

Abstract

We present a perturbation solution for a pressure-driven fluid flow in a rotating toroidal channel. The analysis shows the difference between the solutions of full and simplified equations studied earlier. The result is found to be reliable for {\it low} Reynolds number ($\R$) as was the case for a previously studied solution for high $\R$. The convergence conditions are defined for the whole range of governing parameters. The viscous flow exhibits some interesting features in flow pattern and hydrodynamic characteristics.