scholarly journals Modelling and Analysis of Complex Viscous Fluid in Thin Elastic Tubes

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yufang Gao ◽  
Zongguo Zhang
Keyword(s):  
Cardiovascular Disease ◽  
Blood Flow ◽  
Viscous Fluid ◽  
Boussinesq Equation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Thin Tube ◽  
Elastic Tubes

Cardiovascular disease is a major threat to human health. The study on the pathogenesis and prevention of cardiovascular disease has received special attention. In this paper, we have contributed to the derivation of a mathematical model for the nonlinear waves in an artery. From the Navier–Stokes equations and continuity equation, the vorticity equation satisfied by the blood flow is established. And based on the multiscale analysis and perturbation method, a new model of the Boussinesq equation with viscous term is derived to describe the propagation of a viscous fluid through a thin tube. In order to be more consistent with the flow of the fluid, the time-fractional Boussinesq equation with viscous term is deduced by employing the semi-inverse method and the fractional variational principle. Moreover, the approximate analytical solution of the fractional equation is obtained, and the effect of viscosity on the amplitude and width of the wave is studied. Finally, the effects of the fractional order parameters and vessel radius on blood flow volume are discussed and analyzed.

scholarly journals Time periodic Navier–Stokes equations in a thin tube structure

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
R. Juodagalvytė ◽  
G. Panasenko ◽  
K. Pileckas
Keyword(s):  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Thin Tube ◽  
Time Periodic ◽  
Tube Structure

scholarly journals Dynamic analysis of submerged microscale plates: the effects of acoustic radiation and viscous dissipation

2016 ◽  
Vol 472 (2187) ◽  
pp. 20150728 ◽  
Author(s):  
Zhangming Wu ◽  
Xianghong Ma
Keyword(s):  
Viscous Fluid ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Stokes Equations ◽  
Acoustic Radiation ◽  
Navier Stokes ◽  
Rectangular Plates ◽  
Fluid Loading ◽  
Navier Stokes Equations ◽  
Loading Impedance

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate–fluid interaction problem is developed on the basis of linearized Navier–Stokes equations and no-slip conditions. Analytical expression for the fluid-loading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers being mass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

scholarly journals CENTRIFUGAL DESTABILIZATION AND RESTABILIZATION OF PLANE SHEAR FLOWS

1996 ◽  
Vol 06 (02) ◽  
pp. 409-413
Author(s):  
A. J. CONLEY
Keyword(s):  
Viscous Fluid ◽  
Linear Stability ◽  
Stokes Equations ◽  
Path Following ◽  
Incompressible Viscous Fluid ◽  
Navier Stokes ◽  
Parallel Plates ◽  
Plane Shear ◽  
Navier Stokes Equations ◽  
Spectral Techniques

The flow of an incompressible viscous fluid between parallel plates becomes unstable when the plates are tumbled. As the tumbling rate increases, the flow restabilizes. This phenomenon is elucidated by path-following techniques. The solution of the Navier-Stokes equations is approximated by spectral techniques. The linear stability of these solutions is studied.

Attractors for the modifications of the three-dimensional Navier-Stokes equations

1994 ◽  
Vol 346 (1679) ◽  
pp. 173-190 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Fluid Flows ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Initial Boundary Value ◽  
Dimensional Domain

The modifications of the three-dimensional Navier-Stokes equations, which I suggested earlier for the description of viscous fluid flows with large gradients of velocities, are considered. It is proved that the first initial-boundary value problem for these equations in any bounded three-dimensional domain has a compact minimal global B-attractor. Some properties of the attractor are established.

scholarly journals Simulating of the admixture spreading in a steady 2D lengthy stream of the viscous fluid

2013 ◽  
Vol 2 (1) ◽  
pp. 91-97
Keyword(s):  
Viscous Fluid ◽  
Small Parameter ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computer Experiments ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Convection Diffusion ◽  
Proposed Model ◽  
And Diffusion

The problem of the passive contaminant spreading in a steady viscous fluid stream is discussed while the admixture's dissipation and diffusion are taken into account. The channel is assumed to be a horizontal plane, curvilinear and quite lengthy, so that the ratio of the stream width to its length can be regarded as a small parameter. A mathematical model of the process derived by the small parameter technique from the 2D steady Navier-Stokes equations for incompressible viscous fluid and non-steady convection-diffusion equation of a substance in the moving medium is introduced. A finite element method is applied for numerical study of the proposed model and results of computer experiments are presented.

Stochastic Navier–Stokes equations perturbed by Lévy noise with hereditary viscosity

2019 ◽  
Vol 22 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Manil T. Mohan ◽  
Sivaguru S. Sritharan
Keyword(s):  
Stokes Equations ◽  
Past History ◽  
Local Solvability ◽  
Monotonicity Property ◽  
Three Dimensions ◽  
Navier Stokes ◽  
Lévy Noise ◽  
Navier Stokes Equations ◽  
Viscous Term ◽  
Levy Noise

In this paper, we study the stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise in three dimensions with a hereditary viscous term which depends on the past history. We establish the local solvability of the Cauchy problem for such systems. The local monotonicity property of the nonlinear term of the cutoff problem and a stochastic generalization of the Minty–Browder technique are exploited in the proofs. Finally, we show that the global solvability results hold under smallness condition on the initial data and suitable assumptions on the noise coefficients.

MHD FLOWS DUE TO NON-COAXIAL ROTATIONS OF POROUS DISK AND A VISCOUS FLUID AT INFINITY: GRAPHICAL SOLUTIONS USING MATLAB

2020 ◽  
Vol 9 (11) ◽  
pp. 9287-9301
Author(s):  
R. Lakshmi ◽  
Santhakumari
Keyword(s):  
Velocity Field ◽  
Analytical Solution ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Daily Life ◽  
Vital Role ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Complex Phenomena

Fluids play a vital role in many aspects of our daily life. We drink water, breath air, fluids run through our bodies and it controls the weather. The study of motion of fluids is a complex phenomena. The equations which govern the flows of Newtonian fluids are Navier-Stokes equations. In this paper, the flows which are due to non – coaxial rotations of porous disk and a fluid at infinity are considered. Analytical solution for the velocity field using Laplace transform is derived. MATLAB coding is written to get the graphical solutions. The results are compared with the existing results. MATLAB software provides accurate results depending on the solution we obtained.

INFLUENCE OF FLAT WALL DIFFUSER WALL OSCILLATION ON HYDRODYNAMIC PARAMETERS OF VISCOUS FLUID FLOW

2019 ◽  
Vol 9 (1) ◽  
pp. 119-125
Author(s):  
Evgeny A. KRESTIN
Keyword(s):  
Fluid Flow ◽  
Viscous Fluid ◽  
Stokes Equations ◽  
Hydraulic Drive ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Fluid Flow ◽  
Moving Wall ◽  
Hydrodynamic Parameters

In order to reduce the energy consumption, increase the reliability of the hydraulic drive of construction machines and mechanisms, studies of the hydrodynamic parameters of the viscous fluid flow in a flat diffuser during the oscillation of one of the walls of the channel are carried out. Navier-Stokes equations together with the continuity equation are used to construct velocity and pressure fields. The problem is solved in polar coordinates with boundary conditions. The General solution of the problem, which corresponds to the self-similar boundary condition on the moving wall, is obtained. The radial velocity profile has sections of forward and reverse currents and is a standing wave along the angular coordinate. The forces acting on the movable and stationary walls of the diffuser are determined.

scholarly journals Steady streaming in a channel with permeable walls

2013 ◽  
Vol 25 (1) ◽  
pp. 65-82
Author(s):  
KONSTANTIN ILIN
Keyword(s):  
Asymptotic Expansion ◽  
Viscous Fluid ◽  
Steady Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Stokes Layer ◽  
Permeable Walls ◽  
Time Injection

We study steady streaming in a channel between two parallel permeable walls induced by oscillating (in time) injection/suction of a viscous fluid at the walls. We obtain an asymptotic expansion of the solution of the Navier–Stokes equations in the limit when the amplitude of normal displacements of fluid particles near the walls is much smaller than both the width of the channel and the thickness of the Stokes layer. It is shown that the steady part of the flow in this problem is much stronger than the steady flow produced by vibrations of impermeable boundaries. Another interesting feature of this problem is that the direction of the steady flow is opposite to what one would expect if the flow was produced by vibrations of impermeable walls.

A Parallel Domain Decomposition Algorithm for Simulating Blood Flow with Incompressible Navier-Stokes Equations with Resistive Boundary Condition

2012 ◽  
Vol 11 (4) ◽  
pp. 1279-1299
Author(s):  
Yuqi Wu ◽  
Xiao-Chuan Cai
Keyword(s):  
Boundary Condition ◽  
Blood Flow ◽  
Domain Decomposition ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Outflow Boundary Condition ◽  
Outflow Boundary ◽  
Domain Decomposition Algorithm ◽  
Fully Coupled

AbstractWe introduce and study a parallel domain decomposition algorithm for the simulation of blood flow in compliant arteries using a fully-coupled system of nonlinear partial differential equations consisting of a linear elasticity equation and the incompressible Navier-Stokes equations with a resistive outflow boundary condition. The system is discretized with a finite element method on unstructured moving meshes and solved by a Newton-Krylov algorithm preconditioned with an overlapping restricted additive Schwarz method. The resistive outflow boundary condition plays an interesting role in the accuracy of the blood flow simulation and we provide a numerical comparison of its accuracy with the standard pressure type boundary condition. We also discuss the parallel performance of the implicit domain decomposition method for solving the fully coupled nonlinear system on a supercomputer with a few hundred processors.

Sign in / Sign up

Export Citation Format

Share Document