On the Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) for a nonlinearly stretching sheet flow of Eyring-Powell fluids

Magnetohydrodynamic (MHD) flow due to a nonlinearly stretching sheet acting on non-Newtonian Eyring-Powell fluids inside a Darcy-Forchheimer porous medium is studied. Energy equation is considered subject to 1- Prescribed Surface Temperature 2- Prescribed Surface Heat Flux, both of which with radiation consideration. The resulting similarity equations are tackled analytically by homotopy analysis method, homotopy perturbation method and numerically by 5th order Runge-Kutta and an advanced multistep MATLAB solver. A comparison reveals a remarkable agreement between the solution strategies. Finally, the influence of the involved parameters such as magnetic parameter, Eyring-Powell constitutional constants, Darcy-Forchheimer resistance factors, Prandtl number and radiation parameter is studied in a comprehensive manner. The new considerations in the present research can be summarized as: 1- Lie point symmetry analysis to simply extract the similarity problem. 2- Considering Forchheimer parameter associated with the microscopic inertial effects those leading to significant macroscopic impacts. 3- Different thermal boundary conditions, radiation effect included. 4- A comparative study on several analytical and numerical techniques. 5- A graphical demonstration of the influence of the involved parameters.