scholarly journals Generalized diffusion theory of non-rotational, rigid spherical particle sedimentation in viscous fluid

2001 ◽  
Vol 23 (3) ◽  
pp. 159-166
Author(s):  
Nguyen Hong Phan ◽  
Nguyen Van Diep
Keyword(s):  
Viscous Fluid ◽  
Spherical Particle ◽  
Governing Equation ◽  
Diffusion Theory ◽  
Equation System ◽  
Spherical Particles ◽  
Characteristic Form ◽  
Governing Equations ◽  
Particle Sedimentation ◽  
Mathematical Properties

This paper is devoted to application of Generalized Diffusion Theory for solving a sedimentation problem of rigid spherical particles in viscous fluid. The governing equations have been obtained. It is shown that, in this case the governing equation system is a hyperbolic one, and the equations in the characteristic form have been derived. The mathematical properties of the obtained equation system and the solution for stationary sedimentation where investigated numerically.

scholarly journals A numerical investigation of non-rotational, rigid spherical particle sedimentation problem in viscous fluid

2002 ◽  
Vol 24 (1) ◽  
pp. 46-50
Author(s):  
Nguyen Hong Phan ◽  
Nguyen Van Diep
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Viscous Fluid ◽  
Spherical Particle ◽  
Diffusion Theory ◽  
Physical Phenomenon ◽  
Continuous Part ◽  
Particle Sedimentation ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

This paper can be considered as continuous part of [1], where the generalized diffusion theory of rigid spherical particle sedimentation in viscous fluid was investigated. Here a numerical solution of non-stationary sedimentation process is obtained by using the explicit finite difference method. The obtained results show that this model can be used for qualitative study of physical phenomenon of sedimentation problem.

scholarly journals Governing equations for acid water in canals

1994 ◽  
Vol 16 (4) ◽  
pp. 21-27
Author(s):  
Nguyen Tat Dac
Keyword(s):  
Governing Equation ◽  
Chemical Equilibrium ◽  
Water Movement ◽  
Equation System ◽  
Acid Water ◽  
Governing Equations ◽  
Kinetic Treatment

It is given in this study governing equation system formulation for acid water movement in canals, especially, in the Plain of Reeds of Vietnam where the urbanite equilibrium is found dominant. It is assumed in the model a chemical equilibrium, however a kinetic treatment is also used to deal with dissolution of precipitates and sedimentation.

scholarly journals Generalized diffusion theory of hydrodynamical particle migration in suspensions. Part 1: The case of equal densities

1997 ◽  
Vol 19 (2) ◽  
pp. 9-14
Author(s):  
Nguyen Van Diep
Keyword(s):  
Diffusion Theory ◽  
Continuum Theory ◽  
Equation System ◽  
Particle Migration ◽  
Spherical Particles ◽  
Two Phase Flows ◽  
Two Phase ◽  
Deformable Particles ◽  
Micro Deformation ◽  
General Continuum

The general continuum theory has been developed for two-phase flows of fluid with deformable particles, where the micro-deformation of particles and the relative motion between phases have been taken into account [1-3]. This paper is concerned with using the simplest model from developed general theory for modeling of particle migration in suspensions- one of the most important and complicated aspects of particle-liquid two-phase flows, that has been observed and studied by many authors. For this purpose it is considered the motion of Newtonian fluid-rotating rigid spherical particles two-phase continuum with specialized nonlinear constitutive equations, when the particle and fluid have equal densities. The obtained equation system has been used for studying quantitatively particle migration problem in the circular Couette flow.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

The Influence of Multiple Inclusions on the Cauchy Stress of a Spherical Particle-Reinforced Composite Under Uniaxial Loading

2014 ◽  
Author(s):  
Ke Niu ◽  
Armin Abedini ◽  
Zengtao Chen
Keyword(s):  
Spherical Particle ◽  
Single Particle ◽  
Volume Fraction ◽  
Unit Cell ◽  
Spherical Particles ◽  
Uniaxial Tensile ◽  
Cauchy Stress ◽  
Particle Volume ◽  
Volume Fractions ◽  
Unit Cells

This paper investigates the influence of multiple inclusions on the Cauchy stress of a spherical particle-reinforced metal matrix composite (MMC) under uniaxial tensile loading condition. The approach of three-dimensional cubic multi-particle unit cell is used to investigate the 15 non-overlapping identical spherical particles which are randomly distributed in the unit cell. The coordinates of the center of each particle are calculated by using the Random Sequential Adsorption algorithm (RSA) to ensure its periodicity. The models with reinforcement volume fractions of 10%, 15%, 20% and 25% are evaluated by using the finite element method. The behaviour of Cauchy stress for each model is analyzed at a far-field strain of 5%. For each reinforcement volume fraction, four models with different particle spatial distributions are evaluated and averaged to achieve a more accurate result. At the same time, single-particle unit cell and analytical model were developed. The stress-strain curves of multi-particle unit cells are compared with single-particle unit cells and the tangent homogenization model coupled with the Mori-Tanaka method. Only little scatters were found between unit cells with the same particle volume fractions. Multi-particle unit cells predict higher response than single particle unit cells. As the volume fraction of reinforcements increases, the Cauchy stress of MMCs increases.

THE EFFECTS OF HALL CURRENT ON THE FLOW DUE TO THE OSCILLATING ROTATING POROUS DISK WITH A VISCOUS FLUID AT INFINITY: GRAPHICAL SOLUTIONS USING MATLAB

2021 ◽  
Vol 10 (5) ◽  
pp. 2491-2511
Author(s):  
R. Lakshmi ◽  
A. Santhakumari
Keyword(s):  
Viscous Fluid ◽  
Closed Form ◽  
Hall Current ◽  
Velocity Fields ◽  
Governing Equations ◽  
Porous Disk ◽  
Suction And Blowing

The flow due to the oscillating rotating porous disk with a viscous fluid at infinity is studied under the influence of Hall current. Governing equations are implied with reasonable approximations and solved analytically to get the expressions for the velocity fields in closed form. Graphical results are presented for the velocity components for various values of parameters namely, the Hall, suction and blowing through MATLAB and a discussion is provided. It is important to note that presented results are valid for all values of the frequencies.

Sensitivity Analysis and Optimization of Mechanical System Design

1988 ◽  
Author(s):  
W. J. Langner
Keyword(s):  
Linear Equation ◽  
Mechanical System ◽  
Numerical Integration ◽  
Equation System ◽  
Sensitivity Analyses ◽  
Design Parameters ◽  
Governing Equations ◽  
Integration Algorithm ◽  
Linear Equation System ◽  
The Matrix

Abstract The paper follows studies on simulation of three-dimensional mechanical dynamic systems with the help of sparse matrix and stiff integration numerical algorithms. For sensitivity analyses and the application of numerical optimization procedures it is substantial to calculate the effect of design parameters on the system behaviour by means of derivatives of state variables with respect to the design parameters. For static and quasi static analyses the computation of these derivatives from the governing equations leads to a linear equation system. The matrix of this set of linear equations shows to be the Jacobian matrix required in the numerical integration process solving the system of governing equations for the mechanical system. Thus the factorization of the matrix perfomed by the numerical integration algorithm can be reused solving the linear equation system for the state variable sensitivities. Some example demonstrate the simplicity of building the right hand sides of the linear equation system. Also it is demonstrated that the procedure proposed neatly fits into a modular concept for simulation model building and analysis.

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