Sufficient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable surface in the presence of magnetic field. To achieve this, one parameter linear group transformation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the nonNewtonian fluid (Powell-Eyring model) parameters ε and δ on the skin friction and local heat transfer coefficients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase in ε whereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.

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A theoretical study is made in the region near the stagnation point when a lighter incompressible viscoelastic fluids impinges orthogonally on the surface of another quiescent heavier incompressible viscous fluid. Similarity solutions of the momentum balance equations for both fluids are equalized at the interface. It is noted that an exact boundary layer solution is obtained for the lower lighter fluid. The velocity of the lower fluid is independent of lateral interface velocity but the velocity of the upper viscoelastic fluid increases with increasing lateral interface velocity. It is observed that lateral interface velocity increases with increasing viscoelastic parameter for fixed values of density and viscosity ratio of the two fluids. The convective heat transfer is investigated base on the similarity solutions for the temperature distribution of the two fluids. The interface temperature increases with increasing viscoelastic parameter of the upper viscoelastic fluid.