MHD boundary layer flow of an incompressible upper-convected Maxwell fluid by optimal homotopy asymptotic method

In this article, the magneto-hydrodynamics (MHD) boundary layer flow of an Upper-Convected Maxwell (UCM) fluid has been studied. The governing equations of the MHD boundary layer flow of UCM fluid have been reduced to nonlinear Ordinary Differential Equations (ODEs) by using similarity transformation. The basic idea of Optimal Homotopy Asymptotic Method (OHAM) for the nonlinear ODEs has been presented. The results obtained by OHAM have been compared with those of Homotpy Perturbation Method (HPM) and numerical Boundary Value Problem Method in order to verify accuracy of the proposed method. The effect of the Hartman and Deborah numbers has been discussed. It has been observed that with increase in Hartman number, velocity component steadily decreases and when increasing the magnetic force, thickness of the boundary layer decreases. The obtained solutions show that OHAM is an effective, simpler, easier, and explicit method.