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

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.

Properties of Capturing of Peristaltic Flow to A Chemically Reacting Couple Stress Fluid Through an Inclined Asymmetric Channel with Variable Viscosity and Various Boundaries

“…Mechanism of MHD flow and heat transfer was described by Manjunatha et al [31]. For more details and more applications , we share in this studies the reader to [32,33,34,35,36,37,38] to show effect of analysis for variable viscous through peristaltic tube or channel. In addition, Disu et al [39] the authors considered a porous medium between two vertical wavy with viscosity model.…”

The homotopy analysis Rangaig transform method for nonlinear partial differential equations

“…These efforts have strengthened this area of research through many methods. Among them we find the optimal homotopy asymptotic method and its applications to linear or nonlinear problems of integer order or fractional order [5][6][7], and the homotopy analysis method (HAM). Liao Shijun of Shanghai Jiaotong University created this method in his doctoral dissertation in 1992 [8][9][10].…”