Comptes Rendus
no. 11
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 Fetecau1
1 Department of Mathematics, Technical University of Iasi, R-6600 Iasi, Romania
Comptes Rendus. Mathématique, Volume 335 (2002) no. 11, pp. 979-984.

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 :
Révisé le :
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DOI : 10.1016/S1631-073X(02)02577-3
Constantin Fetecau 1

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

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

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[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

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

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