Asymmetrical slow viscous fluid motions caused by the translation or rotation of two spheres. Part I: The determination of exact solutions for any values of the ratio of radii and separation parameters

1970 ◽  
Vol 21 (2) ◽  
pp. 164-179 ◽  
Author(s):  
Michael E. O'Neill ◽  
R. Majumdar
Keyword(s):  
Viscous Fluid ◽  
Exact Solutions ◽  
Separation Parameters

scholarly journals Analytical Expressions of Hydro-Seismic Forces on Dams

2018 ◽  
Author(s):  
Abdelmadjid Tadjadit ◽  
Boualem Tiliouine
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Upstream Face ◽  
Compressible Viscous Fluid ◽  
Natural Modes ◽  
Boundary Method ◽  
Complete Sets ◽  
Seismic Forces ◽  
Analytical Expressions

Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions.Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions. The formulas obtained for distributions of both shear forces and overturning moments are simple, computationally effective and useful for the preliminary design of dams. They show clearly the separate and combined effects of compressibility and viscosity of water. They also have the advantage of being able to cover a wide range of excitation frequencies even beyond the cut-off frequencies of the natural modes of the reservoir. Key results obtained using the proposed analytical expressions of the hydrodynamic forces are validated using numerical and experimental solutions published for some particular cases available in the specialized literature.

scholarly journals SEPARATION OF MIXTURES By COMBINING RECTIFICATION AND FRACTIONAL CRySTALLIZATION PROCESSES

2017 ◽  
Vol 12 (3) ◽  
pp. 44-51 ◽  
Author(s):  
G. A. Nosov ◽  
M. V. Mikhailov ◽  
A. I. Absattarov
Keyword(s):  
Fractional Crystallization ◽  
Initial Mixture ◽  
Heat Pumps ◽  
Coupled Processes ◽  
Closed Type ◽  
Flow Diagrams ◽  
Separation Of Mixtures ◽  
Separation Parameters ◽  
Effect Of The Composition

Various options of separation of binary mixtures by combining the processes of fractional crystallization and rectification are considered. The base mixture, depending on its composition, can be initially directed to the rectification stage or to one of the stages of separated components crystallization using the proposed variants. The flow diagrams of integrated heat exchanging systems and schemes involving open and closed type heat pumps under consideration for the determination of ways of reducing energy consumption of the coupled processes were suggested. These solutions enable improving the processes energy efficiency. In addition, the analysis of the effect of the composition and temperature of the initial mixture, the temperature of fractionation at the crystallization stage, the composition of distillates and bottom products on the separation parameters was carried out. It was found that when the initial mixture is fed to the stage of crystallization of one of the components, the energy costs for carrying out the process under consideration are usually lower than when the initial mixture is fed to the rectification stage. It is shown that using a combination of fractional crystallization and rectification processes can significantly expand the possible separation range and improve the technical and economic characteristics of the separation process.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

Determination of the Limit Cycle by He’s Parameter-Expansion for Oscillators in a u3 / (1 + u2) Potential

2007 ◽  
Vol 62 (7-8) ◽  
pp. 396-398 ◽  
Author(s):  
Li-Na Zhang ◽  
Lan Xu
Keyword(s):  
Exact Solutions ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Expansion Method ◽  
Nonlinear Oscillators ◽  
Mathematical Tool ◽  
Parameter Expansion ◽  
Parameter Expansion Method ◽  
Powerful Mathematical Tool

This paper applies He’s parameter-expansion method to determine the limit cycle of oscillators in a u3/(1+u2) potential. The results are compared with the exact solutions. This shows that the method is a convenient and powerful mathematical tool for the search of limit cycles of nonlinear oscillators.

scholarly journals Exact solutions of steady planeMHDaligned flows using(ξ,ψ)- or(η,ψ)-coordinates

1997 ◽  
Vol 20 (1) ◽  
pp. 165-186
Author(s):  
F. Labropulu ◽  
O. P. Chandna
Keyword(s):  
Analytic Function ◽  
Exact Solutions ◽  
New Approach ◽  
Steady Plane

A new approach for the determination of exact solutions of steady plane infinitely conductingMHDaligned flows is presented. In this approach, the(ξ,ψ)- or the(η,ψ)- coordinates is used to obtain exact solutions of these flows whereψ=(x,y)is the streamfunction andw=ξ(x,y)+iη(x,y)is an analytic function ofz=x+iy.

scholarly journals On the problem of hydrodynamic stability. I. uniform shearing motion in a viscous fluid

1930 ◽  
Vol 229 (670-680) ◽  
pp. 205-253 ◽  
Keyword(s):  
Viscous Fluid ◽  
Steady Motion ◽  
Precise Determination ◽  
The Body ◽  
Periodic Motions ◽  
Principle Of Superposition ◽  
Moving Body ◽  
Exact Determination ◽  
Shearing Motion

1. Except in a few very simple cases, the equations which govern the motion of a viscous fluid have so far defied analysis. Their difficulty comes mainly from the fact that they are not linear, so that the principle of superposition cannot be employed, as in many branches of mathematical physics, to construct solutions by the method of series or of singularities. For the same reason the flow pattern in the neighbourhood of a moving body must alter when the speed of the body is changed, and it follows that any exact determination of the pattern will be restricted to some definite speed. As a matter of fact, no precise determination of this kind exists, except in cases where the motion is indefinitely slow. But the form of the equations gives no reason for doubting the possibility of “steady” motion (in which the velocities are functions only of position) in every case of flow past fixed and rigid boundaries. Now in experiment it is found (unless the velocities are very small) that eddying or periodic motions always occur. Thus the conclusion seems inevitable that a steady motion may become unstable as the rate of flow is increased, in the sense that accidental disturbances, if of suitable type, will persist.

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