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Present article provides an analytical investigation of the fluid flow and heat and mass transfer for the steady laminar MHD three-dimensional nano-fluid flow over a bi-directional stretching sheet with convective surface boundary condition using Optimal Homotopy analysis method (OHAM). In contrast to the conventional no-slip condition at the surface, Navier's slip condition has been applied. This paper contains two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of Brownian diffusion and thermophoresis simultaneously. The governing partial differential equations (PDEs) are transformed into a highly nonlinear coupled ordinary differential equations (ODEs) consist of the momentum, energy and concentration equations via appropriate similarity transformations. The current OHAM solution demonstrates very good correlation with those of the previously published studies in the especial cases. The influences of different flow physical parameters on all fluid velocity components, temperature distribution and concentration as well as the skin friction coefficients in x and y directions, local Nusselt number and local Sherwood number are tabulated graphically and discussed in details. This study specifies that nano particles in the base fluid offer a potential in increasing the convective heat transfer performance of various liquids. The results show that wall temperature gradient decreases with an increase in thermophoresis parameter or a decrease in Brownian motion parameter. Further, local Sherwood number is inversely proportional to the thermophoresis parameter and also directly proportional to the Brownian motion parameter.

Keywords: MHD, Nano-fluid, Velocity slip, Convective boundary condition, Optimal HAM

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