The Rayleigh–Stokes problem for an edge in an Oldroyd-B fluid

Constantin Fetecau

doi:10.1016/S1631-073X(02)02577-3

The Rayleigh–Stokes problem for an edge in an Oldroyd-B fluid
[Le problème Rayleigh–Stokes pour un dièdre dans un fluide Oldroyd-B]

Constantin Fetecau ¹

¹ Department of Mathematics, Technical University of Iasi, R-6600 Iasi, Romania

Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 979-984.

Résumé
Abstract

Les champs de vitesses correspondant à un fluide de type Oldroyd-B qui exécute un mouvement linéaire dans un dièdre infini sont déterminés pour toutes les valeurs des temps de relaxation et de retard. La solution bien connue pour le fluide de Navier–Stokes, les solutions correspondant à un fluide de Maxwell et à un fluide de grade deux apparaissent comme un cas limite de nos solutions.

The velocity fields corresponding to an incompressible fluid of Oldroyd-B type subject to a linear flow within an infinite edge are determined for all values of the relaxation and retardation times. The well known solution for a Navier–Stokes fluid, as well as those corresponding to a Maxwell fluid and a second grade one, appears as a limiting case of our solutions.

Reçu le : 2002-01-02
Révisé le : 2002-09-12
Publié le : 2002-10-29

DOI : 10.1016/S1631-073X(02)02577-3

Affiliations des auteurs :

Constantin Fetecau ¹

¹ Department of Mathematics, Technical University of Iasi, R-6600 Iasi, Romania

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     title = {The {Rayleigh{\textendash}Stokes} problem for an edge in an {Oldroyd-B} fluid},
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Constantin Fetecau. The Rayleigh–Stokes problem for an edge in an Oldroyd-B fluid. Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 979-984. doi : 10.1016/S1631-073X(02)02577-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02577-3/

Bibliographie
Cité par

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[2] C. Fetecau, J. Zierep, The Rayleigh–Stokes problem for a Maxwell fluid, ZAMP, in press

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[4] J.G. Oldroyd On the formulation of rheological equations of state, Proc. Roy. Soc. London Ser. A, Volume 200 (1950), pp. 53-65

[5] K.R. Rajagopal Mechanics of non-Newtonian fluids, Recent Developments in Theoretical Fluids Mechanics, Pitman Res. Notes Math, 291, Longman, 1993, pp. 129-162

[6] K.R. Rajagopal On boundary conditions for fluids of the differential type, Navier–Stokes Equations and Related Nonlinear Problems, Plenum Press, New York, 1995, pp. 273-278

[7] K.R. Rajagopal; P.N. Kaloni Some remarks on boundary conditions for flows of fluids of the differential type, Cont. Mech. and its Applications, Hemisphere Press, New York, 1989, pp. 935-942

[8] I.N. Sneddon Fourier Transforms, McGraw-Hill, New York, 1951

[9] P.N. Srivastava Non steady helical flow of a visco-elastic liquid, Arch. Mech. Stos, Volume 18 (1966) no. 2, pp. 145-150

[10] J. Zierep Das Rayleigh–Stokes-Problem für die Ecke, Acta Mech, Volume 34 (1979), pp. 161-165

Cité par Sources :

^☆ Dedicated to the memory of Caius Iacob and his Professor Henri Villat.

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