Comparative Analysis of Magnetohydrodynamic Inclined Poiseuille Flow of Couple Stress Fluids

In this paper, the inclined Poiseuille flow of a couple stress fluid between two parallel plates under the influence of a magnetic field is investigated using two analytical techniques: the Homotopy Analysis Method (HAM) and the Optimal Auxiliary Function Method (OAFM). The effects of various non-dimensional parameters on the velocity profile, temperature distribution, shear stresses, and flow rate are analyzed in detail. The solutions obtained from HAM and OAFM are compared through graphical and tabular representations, including residual error analysis. The results demonstrate that OAFM provides a more efficient and accurate solution than HAM. Ultimately, we conclude that both methods are effective in solving highly nonlinear differential equations and complex physical models.