New applications of approximate methods in fluid mechanics

In this paper, we have modeled boundary layer flows induced by continuous stretched surfaces by implementing one of the newest analytical methods of solving nonlinear differential equations called homotopy analysis method (HAM), which gives us a vast freedom to choose the answer type. We have used an iterating analytical method to cope with the nonlinearity. A new adapting boundary condition is proposed in this work that is based on an initial guess and then it is developed to the solution expression. The analytic results are compared with the numerical solution (NS) and the comparison reveals that a good agreement exists between the NS and HAM solution. Also the convergence of the obtained HAM solution is discussed explicitly. The obtained approximate solutions are valid for all values of the dimensionless parameter beta, as it is shown later in the paper. (C) 2010 Curtin University of Technology and John Wiley & Sons, Ltd.