scholarly journals One-dimensional unsteady fluid motion between two infinite walls

2002 ◽  
Vol 14 (7) ◽  
pp. 2572 ◽  
Author(s):  
R. A. Lemdiasov ◽  
V. M. Tenishev ◽  
A. I. Fedoseyev
Keyword(s):  
Fluid Motion ◽  
One Dimensional ◽  
Unsteady Fluid

scholarly journals Filtration of Liquid in a Non-isothermal Viscous Porous Medium

2020 ◽  
pp. 763-773
Author(s):  
Alexander A. Papin ◽  
Margarita A. Tokareva ◽  
Rudolf A. Virts
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
System Of Equations ◽  
One Dimensional ◽  
Unsteady Fluid ◽  
Initial Boundary Value

The solvability of the initial-boundary value problem is proved for the system of equations of one-dimensional unsteady fluid motion in a heat-conducting viscous porous medium

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

scholarly journals Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

2018 ◽  
Vol 45 (2) ◽  
pp. 253-278 ◽  
Author(s):  
Meraj Alam ◽  
Bibaswan Dey ◽  
Sekhar Raja
Keyword(s):  
Solid Tumor ◽  
Solid Phase ◽  
Fluid Motion ◽  
Extracellular Fluid ◽  
Mixture Theory ◽  
Coupled System ◽  
Weak Sense ◽  
Governing Equations ◽  
One Dimensional ◽  
2D And 3D

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska?Brezzi) condition and Lax?Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on ??2 and Sobolev norms. We discuss the so-called phenomena of ?necrosis? inside a solid tumor using the energy of the system.

Floating Membrane Breakwater

1996 ◽  
Vol 118 (1) ◽  
pp. 46-52 ◽  
Author(s):  
A. N. Williams
Keyword(s):  
Wave Reflection ◽  
Structural Parameters ◽  
Unit Length ◽  
Fluid Motion ◽  
Integral Equation Method ◽  
Equation Of Motion ◽  
Boundary Integral ◽  
Mooring Line ◽  
Hydrodynamic Properties ◽  
One Dimensional

The hydrodynamic properties of a flexible floating breakwater consisting of a membrane structure attached to a small float restrained by moorings are investigated theoretically. The tension in the membrane is achieved by hanging a clump weight from its lower end. The fluid motion is idealized as linearized, two-dimensional potential flow and the equation of motion of the breakwater is taken to be that of a one-dimensional membrane of uniform mass per unit length subjected to a constant axial force. The boundary integral equation method is applied to the fluid domain, and the dynamic behavior of the breakwater is also described through an appropriate Green function. Numerical results are presented which illustrate the effects of the various wave and structural parameters on the efficiency of the breakwater as a barrier to wave action. It is found that the wave reflection properties of the structure depend strongly on the membrane length, the magnitude of the clump weight, and the mooring line stiffness, while the membrane weight and excess buoyancy of the system are of lesser importance.

scholarly journals Unsteady Fluid Motion Between Two Infinite Walls Under Variable Body Force

2002 ◽  
Author(s):  
Rostislav Lemdiasov ◽  
Valeriy Tenishev ◽  
Alexander Fedoseyev
Keyword(s):  
Body Force ◽  
Fluid Motion ◽  
Unsteady Fluid

Layer formation in monodispersive suspensions and colloids

1996 ◽  
Vol 328 ◽  
pp. 297-311 ◽  
Author(s):  
A. E. Hosoi ◽  
Todd F. Dupont
Keyword(s):  
Burgers Equation ◽  
Fluid Motion ◽  
Layer Formation ◽  
Dimensional Model ◽  
Qualitative Comparison ◽  
Galerkin Approach ◽  
One Dimensional ◽  
Convection Roll ◽  
Lateral Temperature ◽  
Theoretical Results

We present theoretical results on spontaneous stratification of sedimenting suspensions and colloids caused by a lateral temperature gradient. Fluid motion is treated in the Stokes approximation, and motion of suspended particles is described by Burgers equation with convection. The internal structure and interaction of shocks at convection roll boundaries is studied numerically using a reduced one-dimensional model based on a Galerkin approach. Qualitative comparison is made to experimental data.

On the well-posedness of various one-dimensional model equations for fluid motion

2017 ◽  
Vol 160 ◽  
pp. 25-43 ◽  
Author(s):  
Hantaek Bae ◽  
Dongho Chae ◽  
Hisashi Okamoto
Keyword(s):  
Fluid Motion ◽  
Well Posedness ◽  
Dimensional Model ◽  
One Dimensional ◽  
Model Equations
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