A three-dimensional stretching flow of an Oldroyd fluid
Author:
N. Phan-Thien
Journal:
Quart. Appl. Math. 45 (1987), 23-37
MSC:
Primary 76A05
DOI:
https://doi.org/10.1090/qam/885165
MathSciNet review:
885165
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Abstract: It is shown that a three-dimensional stretching flow of an Oldroyd-type fluid has an exact solution. As the fluid becomes Maxwellian, the solution permits a vortex sheet to propagate from the boundary into the flow domain. Furthermore, it is shown that there exists a critical Weissenberg number above which a stress component increases exponentially with time.
- 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
- Hermann Schlichting, Boundary layer theory, McGraw-Hill, New York; Pergamon Press, London; Verlag G. Braun, Karlsruhe, 1955. Translated by J. Kestin. MR 0076530
N. Phan-Thien, Stagnation flows for the Oldroyd-B fluid, Rheol. Acta 23, 172–176 (1984)
- J. G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. London Ser. A 245 (1958), 278–297. MR 94085, DOI https://doi.org/10.1098/rspa.1958.0083
R. I. Tanner, Engineering rheology, Oxford University Press, London, 1985
N. Phan-Thien, Coaxial-disk flow of an Oldroyd-B fluid: exact solution and stability, J. Non-Newtonian Fluid Mech. 13, 325–340 (1983)
C. Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27, 1915–1917 (1984)
H. Schlichting, Boundary layer theory, trans. J. Kestin, 6th ed., McGraw-Hill, New York, 1968
N. Phan-Thien, Stagnation flows for the Oldroyd-B fluid, Rheol. Acta 23, 172–176 (1984)
J. G. Oldroyd, Non-Newtonian effects in steady motion of some idealized elastico-viscous liquids, Proc. Roy. Soc. London Ser. A 245, 278–297 (1958)
R. I. Tanner, Engineering rheology, Oxford University Press, London, 1985
N. Phan-Thien, Coaxial-disk flow of an Oldroyd-B fluid: exact solution and stability, J. Non-Newtonian Fluid Mech. 13, 325–340 (1983)
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Article copyright:
© Copyright 1987
American Mathematical Society
