The boundary layer on a flat plate in a stream with uniform shear

1961 ◽  
Vol 11 (2) ◽  
pp. 309-316 ◽  
Author(s):  
J. D. Murray
Keyword(s):  
Boundary Layer ◽  
Asymptotic Solution ◽  
Flat Plate ◽  
Pressure Field ◽  
Free Stream ◽  
Main Stream ◽  
Uniform Shear ◽  
Small Viscosity ◽  
Boundary Layer Region ◽  
Layer Region

The incompressible laminar boundary layer on a semi-infinite flat plate is considered, when the main stream has uniform shear. A solution is obtained for the first two terms of an asymptotic solution for small viscosity. It is shown that one of the principal effects of free-stream vorticity is to introduce a modified pressure field outside the boundary-layer region.

scholarly journals A Theory for Wake-Induced Transition

1989 ◽  
Author(s):  
R. E. Mayle ◽  
K. Dullenkopf
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Flow ◽  
Flat Plate ◽  
Free Stream ◽  
Plate Boundary ◽  
Transition Model ◽  
Model Comparisons ◽  
Turbulent Wakes ◽  
Flat Plate Boundary Layer

A theory for transition from laminar to turbulent flow as the result of unsteady, periodic passing of turbulent wakes in the free stream is developed using Emmons’ transition model. Comparisons made to flat plate boundary layer measurements and airfoil heat transfer measurements confirm the theory.

On the flow near the trailing edge of a flat plate

1968 ◽  
Vol 306 (1486) ◽  
pp. 275-290 ◽  
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Governing Equations ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Multiplicative Constant ◽  
Boundary Layer Approximation ◽  
Uniform Shear

It is shown that the boundary layer approximation to the flow of a viscous fluid past a flat plate of length l , generally valid near the plate when the Reynolds number Re is large, fails within a distance O( lRe -3/4 ) of the trailing edge. The appropriate governing equations in this neighbourhood are the full Navier- Stokes equations. On the basis of Imai (1966) these equations are linearized with respect to a uniform shear and are then completely solved by means of a Wiener-Hopf integral equation. The solution so obtained joins smoothly on to that of the boundary layer for a flat plate upstream of the trailing edge and for a wake downstream of the trailing edge. The contribution to the drag coefficient is found to be O ( Re -3/4 ) and the multiplicative constant is explicitly worked out for the linearized equations.

The Effect of Magnetic Field on Compressible Boundary Layer by Homotopy Analysis Method

2021 ◽  
Vol 88 (1-2) ◽  
pp. 125
Author(s):  
R. Madhusudhan ◽  
Achala L. Nargund ◽  
S. B. Sathyanarayana
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Homotopy Analysis Method ◽  
Adverse Pressure Gradient ◽  
Analysis Method ◽  
Boundary Layer Region ◽  
Homotopy Analysis ◽  
Curve Singularities ◽  
Large Injection ◽  
Layer Region

We analyse the effect of applied magnetic field on the flow of compressible fluid with an adverse pressure gradient. The governing partial differential equations are solved analytically by Homotopy analysis method (HAM) and numerically by finite difference method. A detailed analysis is carried out for different values of the magnetic parameter, where suction/ injection is imposed at the wall. It is also observed that flow separation is seen in boundary layer region for large injection. HAM is a series solution which consists of a convergence parameter h which is estimated numerically by plotting <em>h</em> curve. Singularities of the solution are identified by Pade approximation.

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