Velocity Distribution in the Liquid Film During Draining on a Cylindrical Surface

1971 ◽  
Vol 38 (4) ◽  
pp. 795-797
Author(s):  
T. C. Chawla ◽  
H. K. Fauske
Keyword(s):  
Liquid Film ◽  
Velocity Distribution ◽  
Cylindrical Surface ◽  
Initial Period ◽  
Vertical Plane ◽  
Steady State Solution ◽  
Hankel Transform ◽  
Momentum Equation ◽  
Creeping Flow ◽  
Finite Hankel Transform

The solution of the momentum equation describing unsteady creeping flow of the liquid film during its initial period of drainage on a cylindrical surface has been obtained by the method of finite Hankel transform. The steady-state solution describing the later stages of the drainage process [1, 2] has been deduced by letting the time since the start of motion to be infinite. For completeness, the derivation of the velocity distribution for the vertical plane case applying finite sine transform (equivalent of finite Hankel transform for a cylindrical surface) has also been included.

scholarly journals Dual-series equations formulation for static deformation of plates with a partial internal line support

2007 ◽  
Vol 34 (3) ◽  
pp. 221-248 ◽  
Author(s):  
Yos Sompornjaroensuk ◽  
Kraiwood Kiattikomol
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Hankel Transform ◽  
Internal Line ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Load ◽  
Dual Series Equations ◽  
Finite Hankel Transform ◽  
Standard Techniques

The paper deals with the application of dual-series equations to the problem of rectangular plates having at least two parallel simply supported edges and a partial internal line support located at the centre where the length of internal line support can be varied symmetrically, loaded with a uniformly distributed load. By choosing the proper finite Hankel transform, the dual-series equations can be reduced to the form of a Fredholm integral equation which can be solved conveniently by using standard techniques. The solutions of integral equation and the deformations for each case of the plates are given and discussed in details.

Practical numerical considerations for the Alekseev–Mikhailenko method

1990 ◽  
Vol 27 (8) ◽  
pp. 1023-1030 ◽  
Author(s):  
P. F. Daley ◽  
F. Hron
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Integral Transforms ◽  
Hankel Transform ◽  
Radial Symmetry ◽  
Hyperbolic Partial Differential Equations ◽  
Finite Integral ◽  
Finite Hankel Transform ◽  
Difference Methods ◽  
New Generation

Programs that utilize the Alekseev–Mikhailenko method are becoming viable seismic interpretation aids because of the availability of a new generation of supercomputers. This method is highly numerically accurate, employing a combination of finite integral transforms and finite difference methods, for the solution of hyperbolic partial differential equations, to yield the total seismic wave field.In this paper two questions of a numerical nature are addressed. For coupled P–Sv wave propagation with radial symmetry, Hankel transforms of order 0 and 1 are required to cast the problem in a form suitable for solution by finite difference methods. The inverse series summations would normally require that the two sets of roots of the transcendental equations be employed, corresponding to the zeroes of the Bessel functions of order 0 and 1. This matter is clarified, and it is shown that both inverse series summations may be performed by considering only one set of roots.The second topic involves providing practical means of determining the lower and upper bounds of a truncated series that suitably approximates the infinite inverse series summation of the finite Hankel transform. It is shown that the number of terms in the truncated series generally decreases with increasing duration of the source pulse and that the truncated series may be further reduced if near-vertical-incidence seismic traces are avoided.

Generalized finite Hankel transform

2006 ◽  
Vol 17 (1) ◽  
pp. 39-44 ◽  
Author(s):  
Moustafa El-shahed ◽  
M. Shawkey
Keyword(s):  
Hankel Transform ◽  
Finite Hankel Transform

The second-order deformation of a finite compressible isotropic elastic annulus subjected to circular shearing

1993 ◽  
Vol 442 (1916) ◽  
pp. 621-639 ◽  
Keyword(s):  
Hankel Transform ◽  
Outer Edge ◽  
Kernel Functions ◽  
Second Order ◽  
Cylindrical Hole ◽  
Angular Deformation ◽  
Interior Boundary ◽  
Order Deformation ◽  
Finite Hankel Transform

This work investigates the second-order deformation of a uniformly thick compressible isotropic elastic annulus with an axial cylindrical hole. The annulus is clamped at its outer edge and is subjected to a constant angular deformation on the interior boundary of the hole. The implicit m athematical solution is formulated in term s of finite Hankel transform s with Weber-Orr kernel functions which are then numerically inverted.

On a generalized finite Hankel transform

2007 ◽  
Vol 190 (1) ◽  
pp. 705-711 ◽  
Author(s):  
Mridula Garg ◽  
Alka Rao ◽  
S.L. Kalla
Keyword(s):  
Hankel Transform ◽  
Finite Hankel Transform

scholarly journals Pulsating Flow of an Ostwald—De Waele Fluid between Parallel Plates

Water ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 932
Author(s):  
Rodrigo González ◽  
Aldo Tamburrino ◽  
Andrea Vacca ◽  
Michele Iervolino
Keyword(s):  
Shear Stress ◽  
Analytical Solution ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Velocity Distribution ◽  
Momentum Equation ◽  
Parallel Plates ◽  
Analytical Computation ◽  
Pulsatile Pressure ◽  
Pulsatile Pressure Gradient

The flow between two parallel plates driven by a pulsatile pressure gradient was studied analytically with a second-order velocity expansion. The resulting velocity distribution was compared with a numerical solution of the momentum equation to validate the analytical solution, with excellent agreement between the two approaches. From the velocity distribution, the analytical computation of the discharge, wall shear stress, discharge, and dispersion enhancements were also computed. The influence on the solution of the dimensionless governing parameters and of the value of the rheological index was discussed.

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