On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows

The nonlinear boundary value problem describing the nanoboundary-layer flow with linearNavier boundary condition is investigated theoretically and numerically in this paper. TheG′/G-expansion method is applied to search for the all possible exact solutions, and its results arethen validated by the Chebyshev pseudospectral differentiation matrix (ChPDM) approach whichhas been recently introduced and successfully used. This numerical technique is firstlyapplied and, on comparing with the other recent work, it is found that the results are very accurateand effective to deal with the current problem. It is then used to examine and validate the presentanalytical analysis. Although the G′/G-expansion method has been used widely to solve nonlinear wave equations, its application for nonlinear boundary value problems has not been discussed yet, and the present paper may be the first to address this point. It is clarified that the exact solutions obtained via the G′/G-expansion method cannot be obtained by using some of the other methods. In addition, the domain of the physical parameters involved in the current boundary value problem is also discussed. Furthermore, the convex, vicinity of zero, and asymptotic solutions are deduced