Heat and Mass Transfer of Thermophoretic MHD Flow of Powell–Eyring Fluid over a Vertical Stretching Sheet in the Presence of Chemical Reaction and Joule Heating

The present paper deals with the effect of surface heat and mass transfer on magnetohydrodynamic flow of Powell–Eyring fluid over a vertical stretching sheet. The effects of thermophoresis, Joule heating and chemical reaction are also considered. The governing non-linear partial differential equations of the model are transformed into coupled non-linear ordinary differential equations using a similarity transformation and solved numerically by Runge–Kutta method and analytically by homotopy analysis method (HAM). The convergence is carefully checked by plotting $$\hbar $$-curves. For different dimensionless parameters, numerical and analytical calculations are carried out and an investigation of the obtained results shows that the flow field is influenced considerably by the buoyancy ratio and thermal radiation, chemical reaction and magnetic field parameters. A totally analytical and consistently applicable solution is derived which agrees with numerical results.