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.
