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Chaotic Behavior in the Flow Along a Wedge Modeled by the Blasius Equation : Volume 18, Issue 2 (08/03/2011)

By Basu, B.

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Book Id: WPLBN0003982059
Format Type: PDF Article :
File Size: Pages 8
Reproduction Date: 2015

Title: Chaotic Behavior in the Flow Along a Wedge Modeled by the Blasius Equation : Volume 18, Issue 2 (08/03/2011)  
Author: Basu, B.
Volume: Vol. 18, Issue 2
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Historic
Publication Date:
2011
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Basu, B., Sharma, A. S., & Foufoula-Georgiou, E. (2011). Chaotic Behavior in the Flow Along a Wedge Modeled by the Blasius Equation : Volume 18, Issue 2 (08/03/2011). Retrieved from http://worldebookfair.org/


Description
Description: Department of Civil Engineering, University of Minnesota, Minneapolis, MN 55414, USA. The Blasius equation describes the properties of steady-state two dimensional boundary layer forming over a semi-infinite plate parallel to a unidirectional flow field. The flow is governed by a modified Blasius equation when the surface is aligned along the flow. In this paper, we demonstrate using numerical solution, that as the wedge angle increases, bifurcation occurs in the nonlinear Blasius equation and the dynamics becomes chaotic leading to non-convergence of the solution once the angle exceeds a critical value of 22°. This critical value is found to be in agreement with experimental results showing the development of shock waves in the medium and also with analytical results showing multiple solutions for wedge angles exceeding a critical value. Finally, we provide a derivation of the equation governing the boundary layer flow for wedge angles exceeding the critical angle at the onset of chaos.

Summary
Chaotic behavior in the flow along a wedge modeled by the Blasius equation

Excerpt
Schwartz, L. W. and Eley, R. R.: Flow of architectural coatings on complex surfaces theory and experiment, J. Eng. Math., 43, 153–171, 2002.; Adomian, G.: A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135, 501–544, doi:10.1016/0022-247X(88)90170-9, 1988.; Adomian, G.: A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Appl., 21(2), 101–127, doi:10.1016/0898-1221(91)90220-X, 1991.; Adomian, G.: Solution of physical problems by decomposition, Comput. Math. Appl., 27(9–10), 145–154, doi:10.1016/0898-1221(94)90132-5, 1994.; Allan, F. M. and Syam, M. I.: On the analytic solutions of the nonhomogeneous Blasius problem, J. Comput. Appl. Math., 182, 362–371, 2005.; Brighi, B. and Hoernel, J. D.: Recent Advances on Similarity Solutions Arising During Free Convection, Prog. Nonlin., 63, 83–92, 2005.; Brighi, B. and Hoernel, J. D.: Similarity solutions for high frequency excitation of liquid metal in an antisymmetric magnetic field, Banach Center Pub., 74, 41–57, 2006.; Brighi, B. and Sari, T.: Blowing-up coordinates for a similarity boundary layer equation, Discret. Contin. Dyn. S. (DCDS-A), 12(5), 929–948, doi:10.3934/dcds.2005.12.929, 2005.; Cortell, R.: Flow and heat transfer in a moving fluid over a moving flat surface, Theor. Comp. Fluid Dyn., 21(6), 435–446, doi:10.1007/s00162-007-0056-z, 2007.; Fang, T.: Further study on a moving-wall boundary-layer problem with mass transfer, Acta Mech., 163(3–4), 183–188, doi:10.1007/s00707-002-0979-9, 2003a.; Fang, T.: Similarity solutions for a moving-flat plate thermal boundary layer, Acta Mech., 163(3–4), 161–172, doi:10.1007/s00707-003-0004-y, 2003b.; Hussaini, M. Y. and Lakin, W. D.: Existence and non-uniqueness of similarity solutions of a boundary-layer problem, Q. J. Mech. Appl. Math., 39(1), 15–23, doi:10.1093/qjmam/39.1.15, 1986.; Kewley, D. J. and Hornung, H. G.: Non-equilibrium dissociating nitrogen flow over a wedge, J. Fluid Mech., 64(4), 725–736, 1974.; Klemp, J. P. and Acrivos, A.: A moving-wall boundary layer with reverse flow, J. Fluid Mech., 53(1), 177–191, 1972.; Sakiadis, B. C.: Boundary-layer behavior on continuous solid surface: I. Boundary-layer equations for two-dimensional and axisymmetric flow, AIChe J., 7, 26–28, doi:10.1002/aic.690070108, 1961.; Schlichting, H. and Gersten, K: Boundary Layer Theory, 8th rev. edn., McGraw-Hill, New York, 1999.; Schlichting, K. and Bussmann, K.: Exakte Losungen für die laminare Grenzschicht mit Absaugung und Ausblasen, Schriften Deutschen Akademie der Luftfahrtforschung Series B, 7(2), 25–69, 1943 (in German).; Vajravelu, K. and Mohapatra, R. N.: On fluid dynamic drag reduction in some boundary layer flows, Acta Mech., 81, 59–68, doi:10.1007/BF01174555, 1990.; Weyl, H.: On the differential equation of the simplest boundary-layer problems, Ann. Math., 43, 381–407, 1942.; Zaturska, M. B. and Banks, W. H. H.: A new solution branch of the Falkner-Skan equation, Acta Mech., 152, 197–201, doi:10.1007/BF01176954, 2001.

 

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