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1. Introduction
The Blasius equation can be described as the nondimensional velocity distribution in the laminar boundary layer over a flat plate (Blasius, 1908). It describes the similarity solution of the fluid flow influenced by viscous effects. Blasius equation is one of the basic equations of fluid dynamics which describes the velocity profile of the fluid in the boundary layer theory on a half-infinite interval. The Blasius equation is the mother of all boundary layer equations in fluid mechanics.
The well-known nonlinear third-order differential Blasius equation is given by:
(Equation 1)
subject to the initial-boundary conditions:
(Equation 2)
and:
(Equation 3)
The initial-boundary conditions (2) and (3) are that both components of the velocity are zero at the wall due to no slip, and that the horizontal velocity approaches the constant freest ream velocity at some distance away from the plate.
Blasius (1908) found the following approximate analytic solutions in the form of a power series:
(Equation 4)
where:
(Equation 5)
and σ=y ' ' (0), which is valid only for small x.
This problem was solved numerically for the first time by Toepfer by applying a Runge-Kutta method (Toepfer, 1912). A better solution was obtained by Howarth (1938). Howarth’s solution can be reproduced using a numerical boundary value problem solver.
Besides the Blasius method, several approximate methods have been developed for the treatment of the laminar boundary layer. Among these methods are the numerical methods and the integral momentum method (Hughes and Brighton, 1967). The integral method consists of applying Newton’s second law to a control volume that extends along the boundary layer thickness, in such a way that, the sum of the external forces acting on the mentioned volume equals to the total flow of the momentum (Hughes and Brighton, 1967).
Different perturbation methods have been proposed to deal with this nonlinear Blasius equation (Liao, 1997, 1998a, b, 1999a, b, 2011; He, 2003). Parand et al. (2010) also investigated this problem by the Tau method, which reduces the solution of the Blasius equation to the solution of a system of nonlinear equations, Also, the variational iteration method has been applied for this problem. The series solution found in this manner is combined with the diagonal Padé approximants to handle the boundary...