Using Euler-Lagrange Variational Principle to Obtain Flow Relations for Generalized Newtonian Fluids

TL;DR

This paper applies the Euler-Lagrange variational principle to derive flow relations for various generalized Newtonian fluids in cylindrical tubes, providing both analytical and numerical solutions based on stress minimization.

Contribution

It introduces a novel application of the Euler-Lagrange principle to obtain flow relations for multiple non-Newtonian fluid models in a unified framework.

Findings

Derived analytical flow relations for several fluid models

Validated the method with numerical solutions

Applicable to a wide range of non-Newtonian fluids

Abstract

Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration.