Homotopy Solution for Non-Similarity Boundary-Layer Flow near.pdfVIP

Homotopy Solution for Non-Similarity Boundary-Layer Flow near a Stagnation Point Xiangcheng You and Hang Xu State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China Reprint requests to X. Y.; E-mail: xcyou@ Z. Naturforsch. 65a, 161 – 172 (2010); received March 23, 2009 / revised July 3, 2009 In this paper, non-similarity boundary-layer flow of a Newtonian fluid near an asymmetric plane stagnation point with a dimensionless external flow velocity ue = x/(x + 1) is studied. The original boundary-layer equations are transferred into a nonlinear partial differential equation (PDE) with variable coefficients. An analytic technique for strongly nonlinear equations, namely the homotopy analysis method (HAM), is applied to replace the nonlinear PDE by an infinite number of linear ordinary differential equations (ODEs) with constant coefficients. An artificial parameter, called the convergence-control parameter, is introduced to ensure the convergence of solution series. Accurate analytical approximations of skin friction and boundary-layer thickness are obtained, and the effect of the external flow velocity on the non-similarity flows is investigated. This approach has general meanings and can be applied to many other non-similarity boundary-layer flows. Key words: Non-Similarity; Boundary-Layer; Stagnation Point Flow; Series Solution. 1. Introduction is known that most of boundary-layer problems are resolved based on the similarity solutions [10 – 14]. Stagnation point flows are often occurred in sci- However, most boundary-lay