Viscous flow due to a shrinking sheet. (English) Zbl 1169.76018

The authors study the properties of a viscous flow due to a shrinking sheet with suction. Such a flow occurs when the fluid condenses on the surface, as in chemical vapor deposition [see, e.g., K. F. Jensen, E. O. Einset and D. I. Fotiadis, Ann. Rev. Fluid Mech. 23, 197–232 (1991)]. The existence of exact solutions is proved and some discussion about the (non)uniqueness of the exact solution is given. Exact solutions, both numerical and in closed form, are found.


76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35Q30 Navier-Stokes equations
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[1] S. N. Bhattacharyya and A. S. Gupta, On the stability of viscous flow over a stretching sheet, Quart. Appl. Math. 43 (1985), no. 3, 359 – 367. · Zbl 0586.76059
[2] J. F. Brady and A. Acrivos, Steady flow in a channel or tube with an accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow, J. Fluid Mech. 112 (1981), 127 – 150. · Zbl 0491.76037
[3] Crane, L.J. (1970) Flow past a stretching plate. ZAMP 21, 645-647.
[4] Gupta, P.S. and Gupta, A.S. (1977) Heat and mass transfer on a stretching sheet with suction and blowing. Can. J. Chem. Eng. 55, 744-746.
[5] Jensen, K.F., Einset, E.O. and Fotiadis, D.I. (1991) Flow phenomena in chemical vapor deposition of thin films. Ann. Rev. Fluid Mech. 23, 197-232.
[6] J. B. McLeod and K. R. Rajagopal, On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary, Arch. Rational Mech. Anal. 98 (1987), no. 4, 385 – 393. · Zbl 0631.76021
[7] William C. Troy, Edward A. Overman II, G. B. Ermentrout, and James P. Keener, Uniqueness of flow of a second-order fluid past a stretching sheet, Quart. Appl. Math. 44 (1987), no. 4, 753 – 755. · Zbl 0613.76006
[8] Usha, R. and Sridharan, R. (1995) The axisymmetrical motion of a liquid film on an unsteady stretching surface. J. Fluids Eng. 117, 81-85.
[9] C. Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27 (1984), no. 8, 1915 – 1917. · Zbl 0545.76033
[10] Wang, C.Y. (1988) Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466-468.
[11] C. Y. Wang, Liquid film on an unsteady stretching surface, Quart. Appl. Math. 48 (1990), no. 4, 601 – 610. · Zbl 0714.76036
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