Stokes Flow Past an Axially Symmetric Body in a Cylindrical Tube in the Presence of a Magnetic Field

1961 ◽  
Vol 40 (1-4) ◽  
pp. 205-219 ◽  
Author(s):  
I-Dee Chang
Keyword(s):  
Magnetic Field ◽  
Stokes Flow ◽  
Cylindrical Tube ◽  
Symmetric Body ◽  
Axially Symmetric ◽  
Flow Past

Stokes flow of a conducting fluid past an axially symmetric body in the presence of a uniform magnetic field

1960 ◽  
Vol 9 (3) ◽  
pp. 473-477 ◽  
Author(s):  
I-Dee Chang
Keyword(s):  
Magnetic Field ◽  
Stokes Flow ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Magnetic Effect ◽  
Symmetric Body ◽  
Axially Symmetric ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow

Low Reynolds number flow of an incompressible fluid past an axially symmetric body in the presence of a uniform magnetic field is studied using a perturbation method. It is found that for small Hartmann number M an approximate drag formula is given by $ D^ \prime = D^\prime_0 \left(1 + \frac {D^\prime_0} {16\pi \rho vaU}M\right) + O(M^2),$ where D′0 is the Stokes drag for flow with no magnetic effect.

Hydromagnetic Stokes flow past a rotating sphere

1978 ◽  
Vol 88 (4) ◽  
pp. 757-768 ◽  
Author(s):  
V. U. K. Sastry ◽  
K. V. Rama Rao
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Stokes Flow ◽  
Flow Reversal ◽  
Magnetic Pole ◽  
Rotating Sphere ◽  
Flow Past ◽  
Effects Of Rotation ◽  
The Magnetic Field

In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

scholarly journals Shear-free boundary in Stokes flow

1996 ◽  
Vol 19 (1) ◽  
pp. 145-150 ◽  
Author(s):  
D. Palaniappan ◽  
S. D. Nigam ◽  
T. Amaranath
Keyword(s):  
Free Boundary ◽  
Stokes Flow ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Stream Surface ◽  
Flow Past ◽  
Flow Past A Sphere

A theorem of Harper for axially symmetric flow past a sphere which is a stream surface, and is also shear-free, is extended to flow past a doubly-body𝔅consisting of two unequal, orthogonally intersecting spheres. Several illustrative examples are given. An analogue of Faxen's law for a double-body is observed.

Slow viscous flow past a rotating sphere

1971 ◽  
Vol 69 (2) ◽  
pp. 333-336 ◽  
Author(s):  
K. B. Ranger
Keyword(s):  
Stokes Flow ◽  
Rotating Fluid ◽  
Axially Symmetric ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Reversed Flow ◽  
Linear Superposition ◽  
Rotating Sphere ◽  
Flow Past ◽  
Uniform Stream

Keller and Rubinow(l) have considered the force on a spinning sphere which is moving through an incompressible viscous fluid by employing the method of matched asymptotic expansions to describe the asymmetric flow. Childress(2) has investigated the motion of a sphere moving through a rotating fluid and calculated a correction to the drag coefficient. Brenner(3) has also obtained some general results for the drag and couple on an obstacle which is moving through the fluid. The present paper is concerned with a similar problem, namely the axially symmetric flow past a rotating sphere due to a uniform stream of infinity. It is shown that leading terms for the flow consist of a linear superposition of a primary Stokes flow past a non-rotating sphere together with an antisymmetric secondary flow in the azimuthal plane induced by the spinning sphere. For a3n2 > 6Uv, where n is the angular velocity of the sphere, U the speed of the uniform stream, and a the radius of the sphere, there is in the azimuthal plane a region of reversed flow attached to the rear portion of the sphere. The structure of the vortex is described and is shown to be confined to the rear portion of the sphere. A similar phenomenon occurs for a sphere rotating about an axis oblique to the direction of the uniform stream but the analysis will be given in a separate paper.

scholarly journals Steady Stokes flow past dumbbell shaped axially symmetric body of revolution: An analytic approach

2012 ◽  
Vol 39 (3) ◽  
pp. 255-289
Author(s):  
Kumar Srivastava ◽  
Ram Yadav ◽  
Supriya Yadav
Keyword(s):  
Stokes Flow ◽  
Closed Form Expression ◽  
Body Of Revolution ◽  
Axially Symmetric ◽  
Moment Coefficient ◽  
Flow Past ◽  
Flow Situation ◽  
Axis Of Symmetry ◽  
Singularity Distribution ◽  
The Relationship

In this paper, the problem of steady Stokes flow past dumbbell-shaped axially symmetric isolated body of revolution about its axis of symmetry is considered by utilizing a method (Datta and Srivastava, 1999) based on body geometry under the restrictions of continuously turning tangent on the boundary. The relationship between drag and moment is established in transverse flow situation. The closed form expression of Stokes drag is then calculated for dumbbell-shaped body in terms of geometric parameters b, c, d and a with the aid of this linear relation and the formula of torque obtained by (Chwang and Wu, part 1, 1974) with the use of singularity distribution along axis of symmetry. Drag coefficient and moment coefficient are defined in various forms in terms of dumbbell parameters. Their numerical values are calculated and depicted in respective graphs and compared with some known values.

scholarly journals Axisymmertic Stokes flow images in spherical free surfaces with applications to rising bubbles

1983 ◽  
Vol 25 (2) ◽  
pp. 217-231 ◽  
Author(s):  
J. F. Harper
Keyword(s):  
Stokes Flow ◽  
Numerical Solutions ◽  
Free Boundaries ◽  
Rigid Surface ◽  
Axially Symmetric ◽  
Free Surfaces ◽  
Flow Past ◽  
Spherical Bubbles ◽  
Axis Of Symmetry ◽  
First Time

AbstractA theorem is derived for the hydrodynanuc image of an axially symmetric slow viscous (Stokes) flow in a sphere which is impermeable and free of shear stress. A second theorem establishes a sense in which such a flow past an arbitrary rigid surface or shear-free sphere becomes, on inversion in an arbitrary sphere with its centre on the axis of symmetry, a flow past the rigid or shear-free inverse of that surface or sphere.The theorems are used to simplify the proofs of a number of known results for images of point singularities in plane and spherical rigid and free boundaries, and for a pair of bubbles rising steadily in line in a viscous fluid. They also give for the first time accurate numerical solutions for the velocities of each of a larger number of spherical bubbles rising quasi-steadily in line. These enable one to assess the accuracy of simple approximations to those velocities.

Solar Internal Rotation and Dynamo Waves: A Two-Dimensional Asymptotic Solution in the Convection Zone

2000 ◽  
Vol 179 ◽  
pp. 379-380
Author(s):  
Gaetano Belvedere ◽  
Kirill Kuzanyan ◽  
Dmitry Sokoloff
Keyword(s):  
Magnetic Field ◽  
Asymptotic Solution ◽  
Internal Rotation ◽  
Convection Zone ◽  
General Idea ◽  
Dynamo Model ◽  
Axially Symmetric ◽  
Dynamo Action ◽  
Regeneration Rate ◽  
Dynamo Waves

Extended abstractHere we outline how asymptotic models may contribute to the investigation of mean field dynamos applied to the solar convective zone. We calculate here a spatial 2-D structure of the mean magnetic field, adopting real profiles of the solar internal rotation (the Ω-effect) and an extended prescription of the turbulent α-effect. In our model assumptions we do not prescribe any meridional flow that might seriously affect the resulting generated magnetic fields. We do not assume apriori any region or layer as a preferred site for the dynamo action (such as the overshoot zone), but the location of the α- and Ω-effects results in the propagation of dynamo waves deep in the convection zone. We consider an axially symmetric magnetic field dynamo model in a differentially rotating spherical shell. The main assumption, when using asymptotic WKB methods, is that the absolute value of the dynamo number (regeneration rate) |D| is large, i.e., the spatial scale of the solution is small. Following the general idea of an asymptotic solution for dynamo waves (e.g., Kuzanyan & Sokoloff 1995), we search for a solution in the form of a power series with respect to the small parameter |D|–1/3(short wavelength scale). This solution is of the order of magnitude of exp(i|D|1/3S), where S is a scalar function of position.

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