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Math. Comput. Appl. 2010, 15(5), 962-966; doi:10.3390/mca15050962

Analytical Solutions of Nano Boundary Layer Flows by Using He's Homotopy Perturbation Method

1 and 2,*
1
Departments of Mechanical Engineering, Islamic azad university-Sari branch-Sari,Mazandaran, Iran
2
Departments of Civil and Mechanical Engineering, University of Babol Noshivani, Babol, Mazandaran, Iran
*
Author to whom correspondence should be addressed.
Received: 31 December 2010 / Accepted: 31 December 2010 / Published: 31 December 2010
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Abstract

The aim of this article is to examine nano boundary layer. The equations governing the flow on wedge are derived from continuity and Navier-Stoks equations. The boundary conditions for the governing equations are obtained from the nonlinear Navier slip condition. This boundary condition contains an arbitrary index parameter, denoted by n > 0, which appears in the coefficients of the ordinary differential equation to be solved. The coupled equations are transformed into one differential equation by similarity solution. The transformed equation is then solved by He’s Homotopy perturbation method and an analytical solution will be achieved. The validity of results is verified by comparing results with existing numerical results. Results are presented for the x and y components of the velocity profiles. Results are in reasonable agreement with those provided by other numerical methods and demonstrate a good accuracy of the obtained analytical solutions.
Keywords: nano boundary; Homotopy Perturbation Method (HPM); Navier boundary nano boundary; Homotopy Perturbation Method (HPM); Navier boundary
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Khaki, M.; Ganji, D. Analytical Solutions of Nano Boundary Layer Flows by Using He's Homotopy Perturbation Method. Math. Comput. Appl. 2010, 15, 962-966.

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