Variational approach for the flow of Ree-Eyring and Casson fluids in pipes

TL;DR

This paper introduces a variational method to analyze the flow of Ree-Eyring and Casson non-Newtonian fluids in pipes, providing solutions that align with classical analytical models within acceptable error margins.

Contribution

It applies a variational principle to derive flow solutions for Ree-Eyring and Casson fluids, offering an alternative approach to traditional analytical methods.

Findings

Variational solutions match analytical results closely.

Method effectively models non-Newtonian fluid flow in pipes.

Approach offers a new perspective for fluid flow analysis.

Abstract

The flow of Ree-Eyring and Casson non-Newtonian fluids is investigated using a variational principle to optimize the total stress. The variationally-obtained solutions are compared to the analytical solutions derived from the Weissenberg-Rabinowitsch-Mooney equation and the results are found to be identical within acceptable numerical errors and modeling approximations.