Fluid flow induced by a rotating disk of finite radius

Botta, E. F. F.

doi:10.1007/bf00128846

Cited by 7 publications

(10 citation statements)

References 6 publications

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“…In this problem the flow becomes non-axisymmetric due to the presence of the buoyancy force. Some further studies on the rotating flow due to the rotating disk in an ambient fluid were carried out by Vooren and Botta [28], [29], and Tarek et al [30]. In all these analyses, except [27], steady flow was considered.…”

Section: Introductionmentioning

confidence: 99%

Unsteady MHD rotating flow over a rotating sphere near the equator

2003

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Summary. The unsteady rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been studied. The fluid and the body rotate either in the same direction or in opposite directions. The effects of surface suction and magnetic field have been included in the analysis. There is an initial steady state that is perturbed by a sudden change in the rotational velocity of the sphere, and this causes unsteadiness in the flow field. The nonlinear coupled parabolic partial differential equations governing the boundary-layer flow have been solved numerically by using an implicit finite-difference scheme. For large suction or magnetic field, analytical solutions have also been obtained. The magnitude of the radial, meridional and rotational velocity components is found to be higher when the fluid and the body rotate in opposite directions than when they rotate in the same direction. The surface shear stresses in the meridional and rotational directions change sign when the ratio of the angular velocities of the sphere and the fluid k ! k 0 . The final (new) steady state is reached rather quickly which implies that the spin-up time is small. The magnetic field and surface suction reduce the meridional shear stress, but increase the surface shear stress in the rotational direction.

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Section: Introductionmentioning

confidence: 99%

Unsteady MHD rotating flow over a rotating sphere near the equator

2003

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“…(3.4) We now investigate whether the boundary layer exists also for r > 1 as is the case for a rotating disk in a fluid at rest, see van de Vooren and Botta [5]. The boundary conditions (3.3) are replaced outside the disk by…”

Section: The Ekman Layermentioning

confidence: 99%

The Stewartson layer of a rotating disk of finite radius

Vooren

1992

J Eng Math

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It is shown that if a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, an axial layer in the form of a cylindrical shell exists at the edge of the disk. This shell of thickness O(E ~/3) has length O(E -~) in axial direction, where E is the Ekman number. Its most characteristic element is the axial velocity of O(E 1/6) which is larger than everywhere else in the field. We calculate the velocity components and the pressure in this layer.

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“…In the first two equations (2.1) the terms with Re -1 are neglected and the third equation simplifies to dpldz= O. Since it follows, see [1], that --oo for rJ, 1, this theory is not valid in a small region near r = 1. Let us suppose that the size in r-direction of this small region is Re-with a > O0.…”

Section: The Middle Deckmentioning

confidence: 99%

“…In a previous publication [1] the authors have considered the flow outside a rotating disk of finite radius a on the basis of the boundary layer equations. Near the edge of the disk this led to a singularity in the axial velocity w of strength O(r -a) -21 3 for r a, where r is the radial coordinate.…”

Section: Introductionmentioning

confidence: 99%