Damped-Wave Conduction and Relaxation in a Finite Sphere and Cylinder

2008 ◽  
Vol 22 (4) ◽  
pp. 783-786 ◽  
Author(s):  
Kal Renganathan Sharma
Keyword(s):  
Finite Sphere

The three-dimensional hydrodynamic interaction of a finite sphere with a circular orifice at low Reynolds number

1987 ◽  
Vol 174 ◽  
pp. 39-68 ◽  
Author(s):  
Zong-Yi Yan ◽  
Sheldon Weinbaum ◽  
Peter Ganatos ◽  
Robert Pfeffer
Keyword(s):  
Reynolds Number ◽  
Hydrodynamic Interaction ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Series Representation ◽  
Equation Method ◽  
Correction Factors ◽  
Circular Orifice ◽  
Low Reynolds ◽  
Finite Sphere

This paper proposes a combined multipole-series representation and integral-equation method for solving the low-Reynolds-number hydrodynamic interaction of a finite sphere at the entrance of a circular orifice. This method combines the flexibility of the intergral-equation method in treating complicated geometries and the accuracy and computational efficiency of the multipole-series-representation technique. For the axisymmetric case, the hydrodynamic force has been solved for the difficult case where the sphere intersects the plane of the orifice opening, which could not be treated by previous methods. For the three-dimensional case, the first numerical solutions have been obtained for the spatial variation of the twelve force and torque correction factors describing the translation or rotation of the sphere in a quiescent fluid at a pore entrance or the Sampson flow past a fixed sphere. Restricted by excessive computation time, accurate three-dimensional solutions are presented only for a sphere which is one-half the orifice diameter. However, based on an analysis of the behaviour of the force and torque correction factors for this case, approximate interpolation formulas utilizing the results on or near the orifice axis and in the far field are proposed for other diameter ratios, thus greatly extending the usefulness of the present solution.

Coupling and enrichment schemes for finite element and finite sphere discretizations

2005 ◽  
Vol 83 (17-18) ◽  
pp. 1386-1395 ◽  
Author(s):  
Jung-Wuk Hong ◽  
Klaus-Jürgen Bathe
Keyword(s):  
Finite Element ◽  
Finite Sphere

Orbits and rays in the gravitational field of a finite sphere according to the theory of A. N. Whitehead

1952 ◽  
Vol 211 (1106) ◽  
pp. 303-319 ◽  
Keyword(s):  
Gravitational Field ◽  
Continuous Distribution ◽  
Relativity Theory ◽  
Theory Of Relativity ◽  
Test Particles ◽  
Light Rays ◽  
Spherically Symmetric Distribution ◽  
Explicit Formulae ◽  
Finite Sphere ◽  
The Einstein Formula

The relativity theory of A. N. Whitehead permits one to calculate directly the gravitational field of a set of particles of assigned masses and arbitrary motions, and to investigate the orbits of test-particles and the paths of light rays in such a field. In this paper the hypothesis of Whitehead is extended to cover the case of a continuous distribution of matter; the field of a fixed sphere with a spherically symmetric distribution of matter is calculated and orbits and light rays discussed. Explicit formulae are obtained for advance of perihelion, angular velocity in a circular orbit, and deflexion of a light ray. The results differ only slightly from those of Einstein’s general theory of relativity by terms involving the distribution of matter in the sphere, except in the case of the deflexion of light, for which precisely the Einstein formula (depending only on total mass) is obtained.

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