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The flow of nanofluid over a bi-directional stretching sheet is quite popular among recent researchers because of its industrial and engineering applications. Specifically, such a mechanism appears in plastic sheet extrusion, wire drawing, hot rolling, plastic film drawing, paper production, fiber glass, cooling of a metallic plate in a cooling bath, etc. In this paper, we have studied the effects of nanofluid on the flow over a bi-directional stretching sheet for non-Newtonian fluid. Similarity transformations are used to transform the governing partial differential equations into a system of coupled non-linear ordinary differential equations. An optimal homotopy analysis method (OHAM) is employed by defining the average squatted residual errors and the concept of minimization. The effects of different involved physical parameters on the flow field are discussed graphically.