The control problem for linearized two-dimensional wall-bounded parallel shear flows is considered as a means of preventing the laminar-to-turbulent transition. The linearized Navier–Stokes equations are reduced to the Orr– Sommerfeld equation with wall-normal velocity actuation entering through the boundary conditions on the wall. An analysis of the work-energy balance is used to identify appr...

Blasius problem is the simplest nonlinear boundary layer problem. We hope that any approach developed for this epitome can be extended to more difficult hydrodynamics problems. With this motivation we review the so called Töpfer transformation, which allows us to find a non-iterative numerical solution of the Blasius problem by solving a related initial value problem and applying a scaling tran...

In this paper mathematical techniques have been used for the solution of Blasius differential equation. The method uses optimized artificial neural networks approximation with Sequential Quadratic Programming algorithm and hybrid AST-INP techniques. Numerical treatment of this problem reported in the literature is based on Shooting and Finite Differences Method, while our mathematical approach ...

Abstract An explicit approximate solution is obtained for the extended Blasius equation subject to its well-known classical boundary conditions, where viscosity coefficient assumed be positive and temperature-dependent, which arises in several important layer problems fluid dynamics. This problem extends a previous by Cortell (Appl Math Comput 170:706–710, 2005) when constant, numerical was obt...

the purpose of this study is to demonstrate the potential of imperialist competitivealgorithm (ica) for solving blasius dierential equation. this algorithm is inspiredby competition mechanism among imperialists and colonies and has demonstrated excellentcapabilities such as simplicity, accuracy, faster convergence and better global optimumachievement in contrast to other evolutionary algorithms...

The Blasius boundary layer solution is a basic feature of fluid mechanics, and the first application of Prandtl’s boundary layer concept as a significant issue in engineering. This work highlights the contributions of Blasius to hydrodynamics over a period of only six years, which marked the initiation of boundary layer theory. His main papers relating to aerodynamics and smooth turbulent pipe ...