Analysis of couple stress fluid flow with variable viscosity using two homotopy-based methods

Alamgeer Khan,Hanaa Abu-Zinadah,Muhammad Ayaz,Hijaz Ahmad,Muhammad Farooq,Rashid Nawaz,Yu-Ming Chu

doi:10.1515/phys-2021-0015

Abstract

Abstract In this article, the generalized plane Couette flow of Vogel’s model of incompressible, non-isothermal, couple stress fluid flowing steadily between two parallel walls is investigated. The governing equations are reduced to ordinary differential equations. To investigate the non-linear coupled system of differential equations, the optimal homotopy asymptotic method with DJ polynomial and asymptotic homotopy perturbation method have been used. Important flow properties are presented and discussed. We have obtained expressions for velocity, average velocity, shear stress, volume flux and temperature. The results gained employing these techniques are in the form of infinite series; thus, the results can be easily calculated. Comparison of various results, obtained through the suggested approaches, is carried out and an excellent agreement is achieved.

Highlights

In recent decades, the non-Newtonian fluids are very attractive due to their wide range of applications inIn 1966, Stokes for the first time suggested the theory of couple stress fluids [13], which models a fluid medium
The couple stress fluid acknowledged astonishing attention among the numerous models which are utilized to define the non-Newtonian behavior formed by certain fluid [15,16,17] Aksoy [18] studied the entropy generation of couple stress fluid flow
Falade et al [22] employed closed form solutions to examine the influence of variable viscosity on entropy in couple stress fluid flow

Summary

Introduction

The non-Newtonian fluids are very attractive due to their wide range of applications in. Goswami et al [20] have applied the homotopy perturbation transform method to approximate the non-linear fifth order KdV equations. Scientists in refs [23] have examined different couple stress fluid problems of flows past axisymmetric bodies. Goswami et al [24] have investigated the time fractional Kersten–Krasiloshchik coupled KdV–mKdV non-linear system using the homotopy perturbation sumudu transform method. Researchers in refs [35,36] used DJM in the OHAM, for the solution of non-linear differential equations and named this method as OHAM with DJ polynomials. In 2019, Bushnaq et al [38] proposed a new technique to study the non-linear fractional order partial differential equations, which is known as the asymptotic homotopy perturbation method (AHPM).

Basic equations

Description of the methods

Shear stress

Results and discussion

Conclusion