Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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.

References [Enhancements On Off] (What's this?)

  • [1] C. Y. Wang, The three-dimensional flow due to a stretching flat surface, Phys. Fluids 27, 1915-1917 (1984) MR 758728
  • [2] H. Schlichting, Boundary layer theory, trans. J. Kestin, 6th ed., McGraw-Hill, New York, 1968 MR 0076530
  • [3] N. Phan-Thien, Stagnation flows for the Oldroyd-B fluid, Rheol. Acta 23, 172-176 (1984)
  • [4] 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) MR 0094085
  • [5] R. I. Tanner, Engineering rheology, Oxford University Press, London, 1985
  • [6] 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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DOI: https://doi.org/10.1090/qam/885165
Article copyright: © Copyright 1987 American Mathematical Society

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