An Analytic Solution for Electrical Magneto-Hydrodynamics Darcy-Forchheimer Three Dimensional Non-Newtonian Nanofluid Flow with Convective Boundary Conditions

In this article, the treatment of three-dimensional non-Newtonian Williamson fluid has been carried out under examination. Using the standard transformation, the governing equations are converted into universal similarity equations which have been solved by the optimal homotopy asymptotic method. We observed that the method is effective, reliable, consistent and efficient in solving strongly nonlinear differential equations. The influence of embedded parameters on the fluid flow has discovered graphically and using table. The velocity profile in the x-direction is increased with magnetic and electric field parameters and decreased with the increased stretching parameter, coefficient of inertia, velocity slip parameter L-1 and porosity parameters. The velocity profile in the y-direction is increased with magnetic and electric field parameters, the distended stretching parameter, while reduced with the velocity slip parameter L-2, coefficient of inertia, and porosity parameters. The temperature profile is increased with the radiation, thermophoresis and Brownian motion parameters, and Biot number. The profile of concentration is rising with the enlarged Biot numbers and thermophoresis parameter, while reduced with the Brownian motion parameter.