On the second solution of flow of viscoelastic fluid over a stretching sheet
Author:
P. D. Ariel
Journal:
Quart. Appl. Math. 53 (1995), 629-632
MSC:
Primary 76A10; Secondary 76D10
DOI:
https://doi.org/10.1090/qam/1359499
MathSciNet review:
MR1359499
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Abstract: For the boundary layer flow of a viscoelastic fluid caused by the stretching of a sheet, it is demonstrated that, besides the well-known solution, a second solution exists for all nonzero values of $k$, the viscoelastic fluid parameter. This solution is obtained in closed form. It exhibits an oscillatory behavior with the oscillations increasing as $k$ approaches the value zero.
K. R. Rajagopal, T. Y. Na, and A. S. Gupta, Flow of viscoelastic fluid over a stretching sheet, Rheol. Acta 23, 213–215 (1984)
L. J. Crane, Flow past a stretching sheet, Z. Angew. Math. Phys. 21, 645–647 (1970)
J. B. McLeod and K. R. Rajagopal, On the uniqueness of flow of a Navier-Stokes fluid due to stretching boundary, Arch. Rational Mech. Anal. 98, 385–393 (1987)
W. C. Troy, E. A. Overman, II, G. B. Ermentrout, and J. P. Keener, Uniqueness of flow of a second-order fluid past a stretching sheet, Quart. Appl. Math. 44, 753–755 (1987)
P. D. Ariel, A hybrid method for computing the flow of viscoelastic fluids, Internat. J. Numer. Methods Fluids 14, 757–774 (1992)
Wen-Dong Chang, The nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math. 47, 365–366 (1989)
P. D. Ariel, Computation of flow of viscoelastic fluids by parameter differentiation, Internat. J. Numer. Methods Fluids 15, 1295–1312 (1992)
K. R. Rajagopal, T. Y. Na, and A. S. Gupta, Flow of viscoelastic fluid over a stretching sheet, Rheol. Acta 23, 213–215 (1984)
L. J. Crane, Flow past a stretching sheet, Z. Angew. Math. Phys. 21, 645–647 (1970)
J. B. McLeod and K. R. Rajagopal, On the uniqueness of flow of a Navier-Stokes fluid due to stretching boundary, Arch. Rational Mech. Anal. 98, 385–393 (1987)
W. C. Troy, E. A. Overman, II, G. B. Ermentrout, and J. P. Keener, Uniqueness of flow of a second-order fluid past a stretching sheet, Quart. Appl. Math. 44, 753–755 (1987)
P. D. Ariel, A hybrid method for computing the flow of viscoelastic fluids, Internat. J. Numer. Methods Fluids 14, 757–774 (1992)
Wen-Dong Chang, The nonuniqueness of the flow of a viscoelastic fluid over a stretching sheet, Quart. Appl. Math. 47, 365–366 (1989)
P. D. Ariel, Computation of flow of viscoelastic fluids by parameter differentiation, Internat. J. Numer. Methods Fluids 15, 1295–1312 (1992)
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Article copyright:
© Copyright 1995
American Mathematical Society
