Solution of the MHD Falkner-Skan flow by homotopy analysis method

The characteristics of steady two-dimensional laminar boundary layer flow of a viscous and incompressible fluid past a moving wedge with suction or injection are theoretically investigated. The transformed boundary layer equations are solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of Falkner-Skan power-law parameter (m), suction/injection parameter (f0) and the ratio of free stream velocity to boundary velocity parameter (λ) are discussed in detail. The numerical results for velocity distribution and skin friction coefficient are given for several values of these parameters. Comparisons with the existing results obtained by other researchers under certain conditions are made. The critical values off
 0,m and λ are obtained numerically and their significance on the skin friction and velocity profiles is discussed. The numerical evidence would seem to indicate the onset of reverse flow as it has been found by Riley and Weidman in 1989 for the Falkner-Skan equation for flow past an impermeable stretching boundary.

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Falkner-skan equation for flow past a moving wedge with suction or injection

Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions

This paper adopts the differential transformation method to investigate the velocity and shear stress fields associated with the Flakner-Skan boundary-layer problem. A group of transformations are used to reduce the boundary value problem into a pair of initial value problems, which are then solved by means of the differential transformation method. The proposed method yields closed series solutions of the boundary layer equations, which can then be calculated numerically. Numerical results for the dimensionless velocity and the shear stress profiles of the wedge flow are presented graphically for different values of β. It is found that the current results are in good agreement with those provided by other numerical methods. Therefore, the proposed method is proven to be an effective scheme for the solution of nonlinear boundary-layer problems.

N. S. Asaithambi

Papers

A numerical method for the solution of the Falkner-Skan equation

A Galerkin method for Stefan problems

A variable time step Galerkin method for a one-dimensional Stefan problem