Comparative Analysis of the Plane Couette Flow of Couple Stress Fluid Under the Influence of Magnetohydrodynamics

Abstract

The present study aims to perform a comparative analysis of the plane Couette flow of a couple stress fluid under the influence of magnetohydrodynamics (MHD) using two different methods: the Optimal Auxiliary Function Method (OAFM) and the Homotopy Perturbation Method (HPM). The couple stress fluid is known for its non-Newtonian behavior, where the fluid's response to shear is influenced by the presence of internal microstructure. The OAFM and HPM are utlized to solve the governing equations of the couple stress fluid flow under MHD. The OAFM is a numerical technique that involves introducing an auxiliary function to simplify the equations, leading to an easier solution procedure. On the other hand, HPM is an analytical method that employs a series solution . The comparative analysis focuses on examining the accuracy, efficiency, and convergence behavior of the two methods. Various flow parameters such as the couple stress parameter, the magnetic parameter, and the velocity ratio are considered to investigate their influence on the flow behavior. Furthermore the HPM solution was compared with the OAFM solution using different graphs and tables. It reveals that the solution obtained by HPM is batter than OAFM solution.

Keywords

• couple stress fluid
• optimal auxiliary function method (oafm)
• homotopy perturbation method (hpm)
• magnetohydrodynamics (mhd)