A note on flow geometries and the similarity solutions of the boundary layer equations for a nonlinearly stretching sheet

2009 ◽  
Vol 80 (11) ◽  
pp. 1329-1332 ◽  
Author(s):  
Robert A. Van Gorder ◽  
Kuppalapalle Vajravelu
Keyword(s):  
Boundary Layer ◽  
Stretching Sheet ◽  
Similarity Solutions ◽  
Boundary Layer Equations ◽  
Nonlinearly Stretching Sheet

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

Symmetry Analysis of Boundary Layer Equations of an Upper Convected Maxwell Fluid with Magnetohydrodynamic Flow

2011 ◽  
Vol 66 (5) ◽  
pp. 321-328
Author(s):  
Gözde Deǧer ◽  
Mehmet Pakdemirli ◽  
Yiǧit Aksoy
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Boundary Conditions ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Similarity Solutions ◽  
Variable Magnetic Field ◽  
Physical Parameters ◽  
Boundary Layer Equations

Steady state boundary layer equations of an upper convected Maxwell fluid with magnetohydrodynamic (MHD) flow are considered. The strength of the magnetic field is assumed to be variable with respect to the location. Using Lie group theory, group classification of the equations with respect to the variable magnetic field is performed. General boundary conditions including stretching sheet and injection are taken. Restrictions imposed by the boundary conditions on the symmetries are discussed. Special functional forms of boundary conditions for which similarity solutions may exist are derived. Using the symmetries, similarity solutions are presented for the case of constant strength magnetic field. Stretching sheet solutions with or without injection are presented. Effects of physical parameters on the solutions are depicted.

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.

scholarly journals A New Analytical Procedure for Solving the Non-Linear Differential Equation Arising in the Stretching Sheet Problem

2013 ◽  
Vol 18 (3) ◽  
pp. 955-964 ◽  
Author(s):  
P.G. Siddheshwar ◽  
U.S. Mahabaleswar ◽  
H.I. Andersson
Keyword(s):  
Boundary Layer ◽  
Stretching Sheet ◽  
Analytical Procedure ◽  
Boundary Layer Equation ◽  
Newtonian Liquid ◽  
Linear Boundary ◽  
Boundary Layer Equations ◽  
Non Linear ◽  
Clairaut Equation ◽  
Linear Differential

Abstract The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem

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