Differential Transformation Method for solving Falkner-Skan equation to Boundary Layer Flow

Al-Rafidain university college 01/2012; 30.

ABSTRACT n this paper we apply the differential transformation method to solve the third –order boundary value problems characterized by the Falkner-Skan equation over a semi-infinite domain.
The Falkner-Skan equation has two coefficients. Four types of flow in the boundary layer along a surface of revolution near the stagnation point are studied by giving different specific values for coefficients of Falkner-Skan equation. These types of flow are called Blasius flow, Homann axisymmetric stagnation flow, Hiemenz flow, and Homann steady flow.
The effectiveness of the method is illustrated by applying it successfully to various instances of the Falkner-Skan. The differential transformation method show good agreements of results for solving nonlinear BVPs.

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    ABSTRACT: We present a computational method for the solution of the third-order boundary value problem characterized by the well-known Falkner–Skan equation on a semi-infinite domain. Numerical treatments of this problem reported in the literature thus far are based on shooting and finite differences. While maintaining the simplicity of the shooting approach, the method presented in this paper uses a technique known as automatic differentiation, which is neither numerical nor symbolic. Using automatic differentiation, a Taylor series solution is constructed for the initial value problems by calculating the Taylor coefficients recursively. The effectiveness of the method is illustrated by applying it successfully to various instances of the Falkner–Skan equation.
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    ABSTRACT: We present three accurate and efficient numerical schemes for solving the Falkner-Skan equation with positive or negative wall shear. Newton's method is employed, with the aid of the variational equations, in all the schemes and yields quadratic convergence. First, ordinary shooting is used to solve for the case of positive wall shear. Then a nonlinear eigenvalue technique is introduced to solve the inverse problem in which the wall shear is prescribed and the pressure distribution is to be determined. With this approach the reverse flow solutions (i.e., negative wall shear) are obtained. Finally, a parallel shooting method is employed to reduce the sensitivity of the convergence of the iterations to the initial estimates.
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May 16, 2014