Series solutions of nano boundary layer flows by means of the homotopy analysis method |
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Authors: | Jun Cheng RN Mohapatra |
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Institution: | a School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200030, China b Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA |
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Abstract: | We present here a ‘similar’ solution for the nano boundary layer with nonlinear Navier boundary condition. Three types of flows are considered: (i) the flow past a wedge; (ii) the flow in a convergent channel; (iii) the flow driven by an exponentially-varying outer flows. The resulting differential equations are solved by the homotopy analysis method. Different from the perturbation methods, the present method is independent of small physical parameters so that it is applicable for not only weak but also strong nonlinear flow phenomena. Numerical results are compared with the available exact results to demonstrate the validity of the present solution. The effects of the slip length ?, the index parameters n and m on the velocity profile and the tangential stress are investigated and discussed. |
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Keywords: | Boundary layer Nano fluidics Navier boundary condition Homotopy analysis method |
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