Journal ArticleDOI
Boundary layer similarity flow driven by power-law shear
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Similarity solutions of the Prandtl boundary layer equations describing wallbounded flows and symmetric free-shear flows driven by rotational velocities were determined for a range of exponents α and amplitudes β.Abstract:
Similarity solution of the Prandtl boundary layer equations describing wallbounded flows and symmetric free-shear flows driven by rotational velocitiesU(y)=βyα are determined for a range of exponents α and amplitudes β Asymptotic analysis of the equations shows that for α −2/3 the shear stressf″(0) parameter is determined as a function of α and β Symmetric free-shear flow solutions become singular as α→α0 = −1/2 and no solutions are found in the range −1 −1/2 the centerline velocityf′(0) is determined as a function of α and β An asymptotic analysis of the singular behavior of these two problems as α→α0, given in a separate Appendix, shows excellent comparison with the numerical results Similarity solutions at the critical values α0 have exponential decay in the far field and correspond to the Glauert wall jet for wall-bounded flow and to the Schlichting/Bickley planar jet for symmetric free-shear flowread more
Citations
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Transpiration effects on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet with uniform shear flow
TL;DR: In this article, the effect of transpiration on hybrid nanofluid flow and heat transfer over a stretching/shrinking sheet for uniform shear flow was considered, and the similarity equations were attained from the governing equations by using similarity transformation technique, and their solutions were obtained using the bvp4c solver in Matlab software.
Journal ArticleDOI
New similarity solutions of the unsteady incompressible boundary-layer equations
TL;DR: In this article, the Clarkson-Kruskal direct method is used to find similarity reductions of boundary-layer forms to lower-order partial differential systems and to simplify them to the solution of ordinary differential equations.
Journal ArticleDOI
Flow and heat transfer characteristics of the boundary layers over a stretching surface with a uniform-shear free stream
TL;DR: In this article, the momentum and thermal boundary layers over a continuously stretching surface with a uniform-shear free stream were investigated and the similarity equations were obtained based on the boundary layer assumptions, which were solved numerically.
Journal ArticleDOI
The algebraically decaying wall jet
Eugen Magyari,Bruno Keller +1 more
TL;DR: The existence of a self-similar wall jet over a permeable plane surface in the presence of a (suitable) lateral suction of the fluid is proved in this paper.
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Boundary-layer similarity flows driven by a power-law shear over a permeable plane surface
TL;DR: In this paper, the boundary-layer similarity flow driven over a semi-infinite permeable flat plate by a power-law shear with asymptotic velocity profile was considered in the presence of lateral suction or injection of the fluid (y denotes the coordinate normal to the plate).
References
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Journal ArticleDOI
Handbook of Mathematical Functions
Book
Solitons, Nonlinear Evolution Equations and Inverse Scattering
M. A. Ablowitz,Peter A. Clarkson +1 more
TL;DR: In this article, the authors bring together several aspects of soliton theory currently only available in research papers, including inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multidimensional space, and the ∂ method.
Journal ArticleDOI
Errata: Milton Abramowitz and Irene A. Stegun, editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U.S. Government Printing Office, Washington, D.C., 1994, and all known reprints
K. S. Kölbig,F. Schäff +1 more