scholarly journals On Solutions for a Generalized Differential Equation Arising in Boundary Layer Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Sergey Smirnov
Keyword(s):  
Boundary Layer ◽  
Existence And Uniqueness ◽  
Shooting Method ◽  
Boundary Layer Theory ◽  
Boundary Layer Problem ◽  
Blasius Problem ◽  
Generalized Differential Equation ◽  
Generalized Differential ◽  
Uniqueness Of A Solution ◽  
Layer Problem

We treat the existence and uniqueness of a solution for the generalized Blasius problem which arises in boundary layer theory. The shooting method is used in the proof of our main result. An example is included to illustrate the results.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 2: Boundary-Layer Theory Near the Edge

1981 ◽  
Vol 48 (2) ◽  
pp. 383-390 ◽  
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Elastic Plate ◽  
Order Theory ◽  
Higher Order ◽  
Boundary Layer Theory ◽  
Thin Elastic Plate ◽  
Boundary Layer Problem ◽  
Higher Order Theory ◽  
Layer Problem

This paper deals with, as a continuation of Part 1 of this series, the boundary-layer theory for flexural motions of a thin elastic plate. In the framework of the higher-order theory developed in Part 1, three independent boundary conditions at the edge of the plate are too many to be imposed on the essentially fourth order differential equations. To overcome this difficulty, a boundary layer appearing in a narrow region adjacent to the edge is introduced. Using the matched asymptotic expansion method, uniformly valid solutions for a full plate problem are sought. The boundary-layer problem consists of the torsion problem and the plane problem. Three types of the edge conditions are treated, the built-in edge, the free edge, and the hinged edge. Depending on the type of edge condition, the nature of the boundary layer is characterized. After solving the boundary-layer problem, “reduced” boundary conditions relevant to the higher-order theory are established.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

scholarly journals Stability of the laminar boundary layer in a streamwise corner

1984 ◽  
Vol 393 (1804) ◽  
pp. 101-116 ◽  
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Viscous Incompressible Flow ◽  
Boundary Layer Region ◽  
Dimensional Boundary ◽  
The Mean ◽  
Layer Region ◽  
The Stability ◽  
Infinite Boundary Value Problem ◽  
Layer Problem

This work examines the stability of viscous, incompressible flow along a streamwise corner, often called the corner boundary-layer problem. The semi-infinite boundary value problem satisfied by small-amplitude disturbances in the ‘blending boundary layer’ region is obtained. The mean secondary flow induced by the corner exhibits a flow reversal in this region. Uniformly valid ‘first approximations’ to solutions of the governing differ­ential equations are derived. Uniformity at infinity is achieved by a suitable choice of the large parameter and use of an appropriate Langer variable. Approximations to solutions of balanced type have a phase shift across the critical layer which is associated with instabilities in the case of two-dimensional boundary layer profiles.

Application of a General Finite-Difference Method to Boundary Layer Flows

1972 ◽  
Vol 1 (3) ◽  
pp. 146-152
Author(s):  
S. D. Katotakis ◽  
J. Vlachopoulos
Keyword(s):  
Boundary Layer ◽  
Finite Difference ◽  
Boundary Layer Flows ◽  
Boundary Layer Problem ◽  
Boundary Layer Equations ◽  
Temperature Boundary ◽  
Dimensional Boundary ◽  
Finite Difference Solution ◽  
Suction Or Injection ◽  
Layer Problem

A straight-forward and general finite-difference solution of the boundary layer equations is presented. Several problems are examined for laminar flow conditions. These include velocity and temperature boundary layers over a flat plate, linearly retarded flows and several cases of suction or injection. The results obtained are in excellent agreement with existing accurate solutions. It appears that any kind of steady, two-dimensional boundary layer problem can be solved thus with accuracy and speed.

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