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

Mathematical and Computational Applications

Khaki, M.¹ 

关键词: nano boundary;    Homotopy Perturbation Method (HPM);    Navier boundary;   

DOI  :  10.3390/mca15050962

学科分类：计算数学

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY