An approximate solution of the problem of the axially symmetric flow of a viscous incompressible fluid in an angular region

1999 ◽  
Vol 34 (1) ◽  
pp. 133-135
Author(s):  
V. P. Bushlanov
Keyword(s):  
Approximate Solution ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Angular Region

Unsteady Flow in a Porous Medium Between Two Infinite Parallel Plates in Relative Motion

1985 ◽  
Vol 107 (4) ◽  
pp. 534-535 ◽  
Author(s):  
V. M. Soundalgekar ◽  
H. S. Takhar ◽  
M. Singh
Keyword(s):  
Porous Medium ◽  
Approximate Solution ◽  
Unsteady Flow ◽  
Incompressible Fluid ◽  
Phase Angle ◽  
Viscous Incompressible Fluid ◽  
Parallel Plates ◽  
Phase Lead ◽  
Permeability Parameter ◽  
Transient Velocity

An approximate solution to the unsteady flow of a viscous incompressible fluid through a porous medium bounded by two infinite parallel plates, the lower one stationary and the upper one oscillating in its own plane, is presented here. Expressions for the transient velocity, the amplitude, the phase angle α and the skin-friction are derived and numerically calculated. It is observed that the amplitude increases with increasing σ, the permeability parameter, and ω, the frequency. Also, there is always a phase lead, and the phase angle α decreases with increasing σ.

ASYMMETRIC HYDRODYNAMICS OF SUSPENSIONS SUBJECTED TO THE INFLUENCE OF STRONG EXTERNAL MAGNETIC FIELDS

2012 ◽  
Vol 04 (01) ◽  
pp. 1250002
Author(s):  
MAKSYM BEREZHNYI ◽  
EUGEN KHRUSLOV
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Fluid ◽  
Symmetry Axis ◽  
Viscous Incompressible Fluid ◽  
Strain Tensor ◽  
Solid Particles ◽  
Axially Symmetric ◽  
Rotation Tensor ◽  
Small Oscillations ◽  
Homogenized Model

A viscous incompressible fluid with a large number of small axially symmetric solid particles is considered. It is assumed that the particles are identically oriented and under the influence of the fluid they move translationally or rotate around symmetry axis but the direction of their symmetry axes does not change. The asymptotic behavior of small oscillations of the system is studied, when the diameters of particles and distances between the nearest particles are decreased. The equations, describing the homogenized model of the system, are derived. It is shown that the homogenized equations correspond to a non-standard hydrodynamics. Namely, the homogenized stress tensor linearly depends not only on the strain tensor but also on the rotation tensor.

scholarly journals TRANSIENT VISCOUS FLOW IN AN ANNULUS

2002 ◽  
Vol 7 (2) ◽  
pp. 263-270
Author(s):  
A. A. Kolyshkin ◽  
I. Volodko
Keyword(s):  
Approximate Solution ◽  
Laminar Flow ◽  
Incompressible Fluid ◽  
Flow Rate ◽  
Asymptotic Expansions ◽  
Transient Flow ◽  
Viscous Incompressible Fluid ◽  
Time Intervals ◽  
Short Time ◽  
Sudden Reduction

The method of matched asymptotic expansions is used in the present paper to derive an approximate solution for transient flow of a viscous incompressible fluid in an annulus. The transient is caused by a sudden reduction of flow rate to zero. The laminar flow before deceleration can be either steady or unsteady but unidirectional. The solution is valid for short time intervals after sudden deceleration.

scholarly journals An Application of Hankel Transforms in Axially Symmetric Potential Flow

1956 ◽  
Vol 9 (3) ◽  
pp. 128-131
Author(s):  
A. G. Mackie
Keyword(s):  
New York ◽  
Incompressible Fluid ◽  
Circular Hole ◽  
Potential Flow ◽  
Fourier Transforms ◽  
The Other ◽  
Axially Symmetric ◽  
Symmetric Potential ◽  
Physical Interest ◽  
Hankel Transforms

In his book on Hydrodynamics, Lamb obtained a solution for the potential flow of an incompressible fluid through a circular hole in a plane wall. More recently Sneddon (Fourier Transforms, New York, 1951) obtained Lamb's solution by an elegant application of Hankel transforms.Since the streamlines in this solution are symmetric about the wall, it is not of particular physical interest. In this note, Sneddon's method is used to give a solution in which the fluid is infinite in extent on one side of the aperture but issues as a jet of finite diameter on the other side.

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