Similarity solutions for boundary-layer equations with interaction

1983 ◽  
Vol 23 (4) ◽  
pp. 518-522 ◽  
Author(s):  
V. V. Bogolepov ◽  
I. I. Lipatov
Keyword(s):  
Boundary Layer ◽  
Similarity Solutions ◽  
Boundary Layer Equations

The equation of similar profiles in boundary layer theory with strong blowing

1966 ◽  
Vol 294 (1437) ◽  
pp. 208-234 ◽  
Keyword(s):  
Boundary Layer ◽  
Skin Friction ◽  
Main Part ◽  
Similarity Solutions ◽  
Boundary Layer Theory ◽  
Main Stream ◽  
Outer Solution ◽  
Boundary Layer Equations ◽  
Displacement Thickness ◽  
Complicated Form

This paper contains a study of the similarity solutions of the boundary layer equations for the case of strong blowing through a porous surface. The main part of the boundary layer is thick and almost inviscid in these conditions, but there is a thin viscous region where the boundary layer merges into the main stream. The asymptotic solutions appropriate to these two regions are matched to one another when the blowing velocity is large. The skin friction is found from the inner solution, which is independent of the outer solution, but the displacement thickness involves both solutions and is of more complicated form.

scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

A New Approach for the Derivation of the Similarity Equation of the 2-D Unsteady Boundary Layer Equations

2012 ◽  
Author(s):  
Md. Abdus Sattar
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Similarity Solutions ◽  
Length Scale ◽  
Local Similarity ◽  
Unsteady Boundary Layer ◽  
Similarity Equation ◽  
Boundary Layer Equations ◽  
Dimensional Boundary ◽  
The One

A local similarity equation for the hydrodynamic 2-D unsteady boundary layer equations has been derived based on a time dependent length scale initially introduced by the author in solving several unsteady one-dimensional boundary layer problems. Similarity conditions for the potential flow velocity distribution are also derived. This derivation shows that local similarity solutions exist only when the potential velocity is inversely proportional to a power of the length scale mentioned above and is directly proportional to a power of the length measured along the boundary. For a particular case of a flat plate the derived similarity equation exactly corresponds to the one obtained by Ma and Hui[1]. Numerical solutions to the above similarity equation are also obtained and displayed graphically.

Oscillatory solutions of the Falkner-Skan equation

1985 ◽  
Vol 397 (1813) ◽  
pp. 415-418 ◽  
Keyword(s):  
Boundary Layer ◽  
Periodic Solution ◽  
Incompressible Flow ◽  
Symbolic Dynamics ◽  
Similarity Solutions ◽  
Oscillatory Solutions ◽  
Smale Horseshoe ◽  
Boundary Layer Equations ◽  
Prandtl Boundary Layer ◽  
Infinitely Many Periodic Solutions

The Falkner-Skan equation for similarity solutions of the Prandtl boundary-layer equations for incompressible flow is analysed for both positive and negative values of the parameter β . For β < — 1 branches of solutions with any number of intervals of overshoot are found analytically, and confirm recent numerical results. For β > 1 we have proved that there is a periodic solution. We conjecture that for β > 2 there are infinitely many periodic solutions and that a form of ‘symbolic dynamics’, of the kind associated with a Smale ‘horseshoe map’ can be constructed. We have shown this rigorously for β close to 2.

Similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

2009 ◽  
Vol 33 (5) ◽  
pp. 601-606 ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer ◽  
K. Vajravelu ◽  
J. R. Cannon ◽  
Robert A. Van Gorder
Keyword(s):  
Boundary Layer ◽  
Stretching Sheet ◽  
Similarity Solutions ◽  
Boundary Layer Equations ◽  
Nonlinearly Stretching Sheet

Similarity solutions of the two-dimensional unsteady boundary-layer equations

1990 ◽  
Vol 216 ◽  
pp. 537-559 ◽  
Author(s):  
Philip K. H. Ma ◽  
W. H. Hui
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Invariant Solution ◽  
Similarity Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Nonlinear Superposition ◽  
Group Invariant ◽  
Boundary Layer Equations ◽  
Special Cases

The method of Lie group transformations is used to derive all group-invariant similarity solutions of the unsteady two-dimensional laminar boundary-layer equations. A new method of nonlinear superposition is then used to generate further similarity solutions from a group-invariant solution. Our results are shown to include all the existing solutions as special cases. A detailed analysis is given to several classes of solutions which are also solutions to the full Navier–Stokes equations and which exhibit flow separation.

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