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On boundary-layer flows induced by the motion of stretching surfaces

Published online by Cambridge University Press:  18 July 2012

Talal T. Al-Housseiny  and
Howard A. Stone
Talal T. Al-Housseiny
Affiliation:
Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA
Howard A. Stone*
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
*
†Email address for correspondence: [email protected]
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Abstract

We investigate laminar boundary-layer flows due to translating, stretching, incompressible sheets. Unlike the classical problem in the literature where the mechanics of the sheet are neglected, and kinematics are prescribed, the dynamics of both the fluid and the sheet are herein coupled. Two types of stretching sheets are considered: an elastic sheet that obeys linear elasticity and a sheet that deforms as a viscous Newtonian fluid. In both cases, we find self-similar solutions to the coupled fluid/sheet system. These self-similar solutions are only valid under limiting conditions.

JFM classification

Boundary Layers: Boundary Layers Aerodynamics: Flow-structure interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 706 , 10 September 2012 , pp. 597 - 606
Copyright
Copyright © Cambridge University Press 2012

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References

1. Acrivos, A., Shah, M. J. & Petersen, E. E. 1960 Momentum and heat transfer in laminar boundary-layer flows of non-Newtonian fluids past external surfaces. AIChE J. 6, 312–317.CrossRefGoogle Scholar
2. Andersson, H. I. 2002 Slip flow past a stretching surface. Acta Mechanica 158, 121–125.CrossRefGoogle Scholar
3. Andersson, H. I., Aarseth, J. B., Braud, N. & Dandapat, B. S. 1996 Flow of a power-law fluid film on an unsteady stretching surface. J. Non-Newtonian Fluid Mech. 62, 1–8.CrossRefGoogle Scholar
4. Andersson, H. & Kumaran, V. 2006 On sheet-driven motion of power-law fluids. Intl J. Non-Linear Mech. 41, 1228–1234.CrossRefGoogle Scholar
5. Banks, W. H. H. 1983 Similarity solutions of the boundary-layer equations for a stretching wall. J. Méc. Théor. Appl. 2, 375–392.Google Scholar
6. Crane, L. J. 1970 Flow past a stretching plate. J. Appl. Math. Phys. (Z. Angew. Math. Phys.) 21, 645–647.Google Scholar
7. Denn, M. M. 1980 Continuous drawing of liquids to form fibres. Annu. Rev. Fluid Mech. 12, 365–387.CrossRefGoogle Scholar
8. Fang, T., Zhang, J. & Zhong, Y. 2012 Boundary layer flow over a stretching sheet with variable thickness. Appl. Math. Comput. 218, 7241–7252.Google Scholar
9. Fox, V. G., Erickson, L. E. & Fan, L. T. 1969 The laminar boundary layer on a moving continuous flat sheet immersed in a non-Newtonian fluid. AIChE J. 15, 327–333.CrossRefGoogle Scholar
10. Gorla, R. S. R., Dakappagari, V. & Pop, I. 1995 Three-dimensional flow of a power-law fluid due to a stretching flat surface. J. Appl. Math. Mech. (Z. Angew. Math. Mech.) 75, 389–394.CrossRefGoogle Scholar
11. Gupta, P. S. & Gupta, A. S. 1977 Heat and mass transfer on a stretching sheet with suction or blowing. Can. J. Chem. Engng 55, 744–746.CrossRefGoogle Scholar
12. Kumaran, V. & Ramanaiah, G. 1996 A note on the flow over a stretching sheet. Acta Mechanica 116, 229–233.CrossRefGoogle Scholar
13. Lage, J. L. & Bejan, A. 1990 Convection from a periodically stretching plane wall. Trans. ASME: J. Heat Transfer 112, 92–99.CrossRefGoogle Scholar
14. Liao, S. 2006 Series solutions of unsteady boundary-layer flows over a stretching flat plate. Stud. Appl. Math. 117, 239–263.CrossRefGoogle Scholar
15. Magyari, E. 2010 Translation groups of the boundary-layer flows induced by continuous moving surfaces. J. Fluid Mech. 655, 327–343.CrossRefGoogle Scholar
16. Magyari, E. & Keller, B. 1999 Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface. J. Phys. D 32, 2876–2881.CrossRefGoogle Scholar
17. Malvern, L. E. 1969 Introduction to the Mechanics of a Continuous Medium. Prentice Hall.Google Scholar
18. Rajagopal, K. R., Na, T. Y. & Gupta, A. S. 1984 Flow of a viscoelastic fluid over a stretching sheet. Rheol. Acta 23, 213–215.CrossRefGoogle Scholar
19. Rosenhead, L. 1963 Laminar Boundary Layers. Oxford University Press.Google Scholar
20. Sakiadis, B. C. 1961 Boundary-layer behavior on continuous solid surfaces. Part 2. The boundary layer on a continuous flat surface. AIChE J. 7, 221–225.CrossRefGoogle Scholar
21. Scheid, B., Quiligotti, S., Tran, B., Gy, R. & Stone, H. A. 2009 On the (de)stabilization of draw resonance due to cooling. J. Fluid Mech. 636, 155–176.CrossRefGoogle Scholar
22. Surma Devi, C. D., Takhar, H. S. & Nath, G. 1986 Unsteady, three-dimensional, boundary-layer flow due to a stretching surface. Intl J. Heat Mass Transfer 29, 1996–1999.CrossRefGoogle Scholar
23. Vleggaar, J. 1977 Laminar boundary layer behavior on continuous, accelerating surfaces. Chem. Engng Sci. 32, 1517–1525.CrossRefGoogle Scholar
24. Wang, C. Y. 1984 The three-dimensional flow due to a stretching flat surface. Phys. Fluids 27, 1915–1917.CrossRefGoogle Scholar
25. Wang, C. Y. 2002 Flow due to a stretching boundary with partial slip: an exact solution of the Navier–Stokes equations. Chem. Engng Sci. 57, 3745–3747.CrossRefGoogle Scholar
26. Weidman, P. D. & Magyari, E. 2009 Generalized Crane flow induced by continuous surfaces stretching with arbitrary velocities. Acta Mechanica 209, 353–362.CrossRefGoogle Scholar