A new Technique for Solution of the Blasius and Falkner-Skan Boundary Layer Equations

摘要

The Blasius equation describing viscous flow over a flat plate has fascinated physicists, engineers, mathematicians and numerical analysts alike. This ODE is rich in physical, mathematical and numerical challenges. Because of its application to fluid flow, physicists and engineers have a keen interest in solving the Blasius equation and the related, but more general, Falkner-Skan (F-S) equation. In the present paper, the Falkner-Skan (F-S) equation is solved using a new technique based on Taylor theory with shooting algorithm. The Falkner-Skan equation has two coefficients β_0 and β, which corresponding to different types of flows. The 3rd order differential Falkner-Skan (F-S) equation is solved with different values of β_0 and β using Matlab software. The results of the present technique are compared with the published results. Comparison shows an excellent agreement with the results that found in the literature.