In the present paper, a solution for the boundary value problem over a semi-infinite interval has been obtained by transforming the two-dimensional laminar boundary equations into a nonlinear ordinary equation using similarity variables. Moreover, a collocation method is proposed to solve the Falkner-Skan equation. This method is based on rational Legendre functions and convert the Falkner-Skan...

The magnetohydrodynamic (MHD) Falkner-Skan equations appear in study of laminar boundary layers flow over a wedge in presence of a transverse magnetic field. The partial differential equations of boundary layer problems in presence of a transverse magnetic field are reduced to MHD Falkner-Skan equation by similarity solution methods. This is a nonlinear ordinary differential equation. In this p...

The Falkner-Skan equation is a nonlinear third-order boundary value problem defined on the semi-infinite interval [0,∞). This equation plays an important role to illustrate the main physical features of boundary layer phenomena. This paper presents a new collocation method for solving the Falkner-Skan equation. The proposed approach is equipped by the orthogonal Chebyshev polynomials that have ...

One of the well-known schemes for direct numerical integration second-order initial-value problems is due to Falkner. This paper focuses on construction a family adapted block Falkner methods which are frequency dependent solution initial value with oscillatory solutions. The techniques collocation and interpolation adopted here derive new methods. study properties proposed reveals that they co...

A novel method based on Genetic Algorithm to solve the boundary value problems (BVPs) of the Falkner–Skan equation over a semi-infinite interval has been presented. In our approach, we use the free boundary formulation to truncate the semi-infinite interval into a finite one. Then we use the shooting method based on Genetic Algorithm to transform the BVP into initial value problems (IVPs). Gene...

The Falkner-Skan equation arises in the study of laminar boundary layers exhibiting similarity. The MHD systems are used effectively in many applications including power generators, pumps, accelerators, electrostatic filters, droplet filters, the design of heat exchangers, the cooling of reactors, etc. For the MHD Falkner-Skan equation, we have developed a new numerical technique transforming t...

This article is a review of ongoing research on analytical, numerical, and mixed methods for the solution third-order nonlinear Falkner–Skan boundary-value problem, which models non-dimensional velocity distribution in laminar boundary layer.

in the age of technology, it is vital to cool down different parts of a device to use it more beneficially. using nanofluids is one of the most common methods which has shown very effective results. in this paper, we have rephrased a classic equation in fluid mechanics, i.e. the falkner-skan boundary layer equation, in order to be used for nanofluid. this nonlinear equation, which was presented...