Analytic Approximate Solutions for MHD Boundary-Layer Viscoelastic Fluid Flow over Continuously Moving Stretching Surface by Homotopy Analysis Method with Two Auxiliary Parameters

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method HAM with two auxiliary parameters for two classes of visco-elastic fluid Walters’ liquid B and second-grade fluid . It is clear that by the use of second auxiliary parameter, the straight line region in -curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: a prescribed surface temperature PST and b prescribed heat flux PHF . The effect of involved parameters on velocity and temperature is investigated.