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Research Papers

A Novel Similarity Transformation for the Boundary Layer Equations: Solution of Boundary Layer Flows Subjected to Exponential Outer Velocity Profiles

[+] Author and Article Information
S. J. Karabelas

Department of Chemical Engineering, National Technical University of Athens (NTUA), Computational Fluid Dynamics Unit, 157 80 Athens, Greecestkarabelas@gmail.com

J. Appl. Mech 78(4), 041012 (Apr 13, 2011) (5 pages) doi:10.1115/1.4003770 History: Received July 17, 2010; Revised March 07, 2011; Posted March 08, 2011; Published April 13, 2011; Online April 13, 2011

A new similarity transformation applies to the boundary layer equations, which govern laminar, steady, and incompressible flows. This transformation is proved to be more consistent and more complete than the well known Falkner–Skan transformation. It applies to laminar, incompressible, and steady boundary layer flows with a power-law ue(x)=cxm or exponential profile ue(x)=cemx of the outer velocity. This family of “similar solutions” is resolved for various values of the exponent m. A physical interpretation of these velocity profiles is presented, and conclusions are drawn regarding the tolerance of these boundary layers to flow separation under an adverse pressure gradient.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Dimensionless streamwise velocity versus Blasius (top) and the present similarity variable (bottom)

Grahic Jump Location
Figure 2

Dimensionless streamwise velocity versus eη/2=ue/νy, where η=ln(uey2/v) at different values of the exponent m. Bottom: velocity vector field for U(x)=ex.

Grahic Jump Location
Figure 3

Velocity vector field for U(x)=e−x

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