An efficient algorithm of solution for the flow of generalized Newtonian fluid in channels of simple geometries

TL;DR

This paper presents a highly efficient and adaptable algorithm for solving stationary flow problems of generalized Newtonian fluids in simple channel geometries, combining continuous viscosity approximation with analytical integration.

Contribution

It introduces a flexible, low-cost computational scheme that accurately models generalized Newtonian fluid flow in various simple geometries, including circular and elliptic channels.

Findings

Algorithm achieves high accuracy with low computational cost

Versatile method adaptable to different conduit shapes

Validated with Carreau fluid example

Abstract

In this paper a problem of stationary flow of generalized Newtonian fluid in a thin channel is considered. An efficient algorithm of solution is proposed that includes a flexible procedure for a continuous approximation of the apparent viscosity by means of elementary functions combined with analytical integration of the governing equations. The algorithm can be easily adapted to circular or elliptic conduits. The accuracy and efficiency of computations are analyzed using an example of the Carreau fluid. The proposed computational scheme proves to be highly efficient and versatile providing excellent accuracy of solution at a very low computational cost.