The Boundary-Layer Equation for Axially Symmetric Flow Past a Body of Revolution - Motion of a Sphere

1958 ◽  
Vol 25 (10) ◽  
pp. 631-634 ◽  
Author(s):  
DAVID MEKSYN
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Equation ◽  
Body Of Revolution ◽  
Axially Symmetric ◽  
Symmetric Flow ◽  
Flow Past

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.

Numerical integration of the boundary-layer equation

1951 ◽  
Vol 209 (1098) ◽  
pp. 375-379
Keyword(s):  
Boundary Layer ◽  
Numerical Integration ◽  
Satisfactory Agreement ◽  
Boundary Layer Equation ◽  
Elliptic Cylinder ◽  
Successive Approximations ◽  
Flow Past

The boundary-layer equation is integrated step by step and by successive approximations, and applied to Schubauer’s measurements of flow past an elliptic cylinder; the results obtained are in satisfactory agreement with the measurements.

Aligned-field hydromagnetic flow past a slender body

1966 ◽  
Vol 25 (2) ◽  
pp. 289-298 ◽  
Author(s):  
S. Leibovich ◽  
G. S. S. Ludford
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Steady State ◽  
Steady State Solution ◽  
Axially Symmetric ◽  
Hydromagnetic Flow ◽  
Symmetric Flow ◽  
New Approach ◽  
Very High ◽  
Initial Magnetic Field

This is a continuation of our previous work (1965) on the Sears–Resler–Stewartson controversy, in the context of axially symmetric flow. A new approach is presented using boundary-layer arguments, which remove much of the old complexity.For resistive bodies of shape R(x) we uncover a similarity with plane airfoils of shape F(x) = R2(x). As before, Stewartson's slug flows develop fore and aft. For bodies of very high conductivity the Sears–Resler (steady-state) solution turns out to be one possibility. It pertains to bodies (of much higher conductivity than the liquid) into which the initial magnetic field has not diffused.

NATURAL CONVECTION BOUNDARY LAYER FLOW PAST A FLAT PLATE OF FINITE DIMENSIONS

2012 ◽  
Vol 15 (6) ◽  
pp. 585-593
Author(s):  
M. Jana ◽  
S. Das ◽  
S. L. Maji ◽  
Rabindra N. Jana ◽  
S. K. Ghosh
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Flat Plate ◽  
Boundary Layer Flow ◽  
Convection Boundary Layer ◽  
Flow Past ◽  
Convection Boundary ◽  
Layer Flow
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