Viscous flow due to a shrinking sheet
Authors:
M. Miklavčič and C. Y. Wang
Journal:
Quart. Appl. Math. 64 (2006), 283-290
MSC (2000):
Primary 76D03, 76D05, 34B15
DOI:
https://doi.org/10.1090/S0033-569X-06-01002-5
Published electronically:
April 6, 2006
MathSciNet review:
2243864
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.
- 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. MR 814233, DOI https://doi.org/10.1090/S0033-569X-1985-0814233-X
- 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. MR 639234, DOI https://doi.org/10.1017/S0022112081000323
c Crane, L.J. (1970) Flow past a stretching plate. ZAMP 21, 645-647.
gg 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.
je 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.
- 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. MR 872753, DOI https://doi.org/10.1007/BF00276915
- 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. MR 872826, DOI https://doi.org/10.1090/S0033-569X-1987-0872826-3
us Usha, R. and Sridharan, R. (1995) The axisymmetrical motion of a liquid film on an unsteady stretching surface. J. Fluids Eng. 117, 81-85.
- C. Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27 (1984), no. 8, 1915–1917. MR 758728, DOI https://doi.org/10.1063/1.864868
w2 Wang, C.Y. (1988) Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466-468.
- C. Y. Wang, Liquid film on an unsteady stretching surface, Quart. Appl. Math. 48 (1990), no. 4, 601–610. MR 1079908, DOI https://doi.org/10.1090/qam/1079908
bg Bhattacharyya, S.N. and Gupta, A.S. (1985) On the stability of viscous flow over a stretching sheet. Quart. Appl. Math. 43, 359-367.
ba Brady, J.F. and Acrivos, A. (1981) Steady flow in a channel or tube with accelerating surface velocity. An exact solution to the Navier-Stokes equations with reverse flow. J. Fluid Mech. 112, 127-150.
c Crane, L.J. (1970) Flow past a stretching plate. ZAMP 21, 645-647.
gg 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.
je 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.
mr McLeod, J.B. and Rajagopal, K.R. (1987) On the uniqueness of flow of a Navier-Stokes fluid due to a stretching boundary. Arch. Rat. Mech. Anal. 98, 385-393.
to Troy, W., Overman II, E.A., Ermentrout, G.B. and Keener, J.P. (1987) Uniqueness of flow of a second-order fluid past a stretching sheet. Quart. Appl. Math. 44, 753-755.
us Usha, R. and Sridharan, R. (1995) The axisymmetrical motion of a liquid film on an unsteady stretching surface. J. Fluids Eng. 117, 81-85.
w1 Wang, C.Y. (1984) The three-dimensional flow due to a stretching flat surface. Phys. Fluids 27, 1915-1917.
w2 Wang, C.Y. (1988) Fluid flow due to a stretching cylinder. Phys. Fluids 31, 466-468.
w3 Wang, C.Y. (1990) Liquid film on an unsteady stretching sheet. Quart. Appl. Math. 48, 601-610.
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC (2000):
76D03,
76D05,
34B15
Retrieve articles in all journals
with MSC (2000):
76D03,
76D05,
34B15
Additional Information
M. Miklavčič
Affiliation:
Dept. of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
milan@math.msu.edu
C. Y. Wang
Affiliation:
Dept. of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email:
cywang@math.msu.edu
Received by editor(s):
July 6, 2005
Published electronically:
April 6, 2006
Article copyright:
© Copyright 2006
Brown University
The copyright for this article reverts to public domain 28 years after publication.
