scholarly journals An Analysis of the Flow of a Newtonian Fluid between Two Moving Parallel Plates

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
A. Zeb ◽  
A. M. Siddiqui ◽  
M. Ahmed
Keyword(s):  
Stream Function ◽  
Newtonian Fluid ◽  
Constant Velocity ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Fluid Pressure ◽  
Parallel Plates ◽  
Incompressible Newtonian Fluid ◽  
Inverse Solutions ◽  
Analytical Expressions

We consider flow of an incompressible Newtonian fluid produced by two parallel plates, moving towards and away from each other with constant velocity. Inverse solutions of the equations of motion are obtained by assuming certain forms of the stream function. Analytical expressions for the stream function, fluid velocity components, and fluid pressure are derived.

Studying the Blood Plasma Flow past a Red Blood Cell with the Mathematical Method of Kelvin's Transformation

2014 ◽  
Vol 2 (1) ◽  
pp. 57-66
Author(s):  
Maria Hadjinicolaou ◽  
Eleftherios Protopapas
Keyword(s):  
Blood Cell ◽  
Blood Plasma ◽  
Stream Function ◽  
Plasma Flow ◽  
Red Blood Cell ◽  
Fluid Velocity ◽  
Prolate Spheroid ◽  
Mathematical Tool ◽  
Flow Past ◽  
Analytical Expressions

A mathematical tool, namely the Kelvin transformation, has been employed in order to derive analytical expressions for important hydrodynamic quantities, aiming to the understanding and to the study of the blood plasma flow past a Red Blood Cell (RBC). These quantities are the fluid velocity, the drag force exerted on a cell and the drag coefficient. They are obtained by employing the stream function ? which describes the Stokes flow past a fixed cell. The RBC, being a biconcave disk, has been modelled as an inverted prolate spheroid. The stream function is given as a series expansion in terms of Gegenbauer functions, which converge fast. Therefore we employ only the first term of the series in order to derive simple and ready to use analytical expressions. These expressions are important in medicine, for studying, for example the transportation of oxygen, or the drug delivery to solid tumors.

scholarly journals A Hybrid Approach for the Simulation of the Thermal Motion of a Nearly Neutrally Buoyant Nanoparticle in an Incompressible Newtonian Fluid Medium

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
B. Uma ◽  
R. Radhakrishnan ◽  
D. M. Eckmann ◽  
P. S. Ayyaswamy
Keyword(s):  
Newtonian Fluid ◽  
Brownian Particle ◽  
Equations Of Motion ◽  
Hybrid Approach ◽  
Thermal Motion ◽  
Fluctuating Hydrodynamics ◽  
Arbitrary Lagrangian Eulerian ◽  
Fluid Medium ◽  
Incompressible Newtonian Fluid ◽  
Neutrally Buoyant

A hybrid approach consisting of a Markovian fluctuating hydrodynamics of the fluid and a non-Markovian Langevin dynamics with the Ornstein–Uhlenbeck noise perturbing the translational and rotational equations of motion of a nanoparticle is employed to study the thermal motion of a nearly neutrally buoyant nanoparticle in an incompressible Newtonian fluid medium. A direct numerical simulation adopting an arbitrary Lagrangian–Eulerian based finite element method is employed for the simulation of the hybrid approach. The instantaneous flow around the particle and the particle motion are fully resolved. The numerical results show that (a) the calculated temperature of the nearly neutrally buoyant Brownian particle in a quiescent fluid satisfies the equipartition theorem; (b) the translational and rotational decay of the velocity autocorrelation functions result in algebraic tails, over long time; (c) the translational and rotational mean square displacements of the particle obey Stokes–Einstein and Stokes–Einstein–Debye relations, respectively; and (d) the parallel and perpendicular diffusivities of the particle closer to the wall are consistent with the analytical results, where available. The study has important implications for designing nanocarriers for targeted drug delivery. A major advantage of our novel hybrid approach employed in this paper as compared to either the fluctuating hydrodynamics approach or the generalized Langevin approach by itself is that only the hybrid method has been shown to simultaneously preserve both hydrodynamic correlations and equilibrium statistics in the incompressible limit.

An Investigation of a Squeeze Film Between Two Plane Annuli

1998 ◽  
Vol 120 (3) ◽  
pp. 610-615 ◽  
Author(s):  
R. Usha ◽  
Rukmani Sridharan
Keyword(s):  
Reynolds Number ◽  
Power Series ◽  
Newtonian Fluid ◽  
Constant Velocity ◽  
Load Capacity ◽  
Finite Amplitude ◽  
Squeeze Flow ◽  
Squeeze Film ◽  
Harmonic Oscillations ◽  
Incompressible Newtonian Fluid

An analysis of a laminar squeeze flow of an incompressible Newtonian fluid between parallel plane annuli is presented. The local and convective inertia of the flow are considered in the investigation. The solution is obtained as a power series in a single nondimensional parameter (squeeze Reynolds number) S, for small values of S. Expressions for the pressure and load capacity are given and are compared with those based on the assumption of inertialess flow. As applications, the constant velocity squeezing state and the case when the walls perform reciprocating harmonic oscillations with finite amplitude are considered. The changes in load capacity with the changes in the parameters that govern the motion have been investigated.

scholarly journals The Effect of Wall Shear Stress on Two Phase Fluctuating Flow of Dusty Fluids by Using Light Hill Technique

Water ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1587
Author(s):  
Dolat Khan ◽  
Ata ur Rahman ◽  
Gohar Ali ◽  
Poom Kumam ◽  
Attapol Kaewkhao ◽  
...  
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Base Fluid ◽  
Perturbation Technique ◽  
Fluid Velocity ◽  
Dust Particles ◽  
Stress Effect ◽  
Parallel Plates ◽  
Dusty Fluid ◽  
Wall Shear

Due to the importance of wall shear stress effect and dust fluid in daily life fluid problems. This paper aims to discover the influence of wall shear stress on dust fluids of fluctuating flow. The flow is considered between two parallel plates that are non-conducting. Due to the transformation of heat, the fluid flow is generated. We consider every dust particle having spherical uniformly disperse in the base fluid. The perturb solution is obtained by applying the Poincare-Lighthill perturbation technique (PLPT). The fluid velocity and shear stress are discussed for the different parameters like Grashof number, magnetic parameter, radiation parameter, and dusty fluid parameter. Graphical results for fluid and dust particles are plotted through Mathcad-15. The behavior of base fluid and dusty fluid is matching for different embedded parameters.

A Second Order Lagrangian Model for Irregular Ocean Waves

2005 ◽  
Vol 128 (3) ◽  
pp. 177-183 ◽  
Author(s):  
Sébastien Fouques ◽  
Harald E. Krogstad ◽  
Dag Myrhaug
Keyword(s):  
Specular Reflection ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Wave Theory ◽  
Ocean Waves ◽  
Second Order ◽  
Lagrangian Model ◽  
Lagrangian Description ◽  
Linear Wave ◽  
Irregular Solution

Synthetic aperture radar (SAR) imaging of ocean waves involves both the geometry and the kinematics of the sea surface. However, the traditional linear wave theory fails to describe steep waves, which are likely to bring about specular reflection of the radar beam, and it may overestimate the surface fluid velocity that causes the so-called velocity bunching effect. Recently, the interest for a Lagrangian description of ocean gravity waves has increased. Such an approach considers the motion of individual labeled fluid particles and the free surface elevation is derived from the surface particles positions. The first order regular solution to the Lagrangian equations of motion for an inviscid and incompressible fluid is the so-called Gerstner wave. It shows realistic features such as sharper crests and broader troughs as the wave steepness increases. This paper proposes a second order irregular solution to these equations. The general features of the first and second order waves are described, and some statistical properties of various surface parameters such as the orbital velocity, slope, and mean curvature are studied.

Vibration and Stability Behaviour of Sandwiched Viscoelastic Pipes Conveying a Non-Newtonian Fluid

2010 ◽  
Author(s):  
Vincent O. S. Olunloyo ◽  
Charles A. Osheku ◽  
Sidikat I. Kuye
Keyword(s):  
Newtonian Fluid ◽  
Fluid Velocity ◽  
Linear Equations ◽  
Steel Pipes ◽  
Flow Parameters ◽  
Internal Fluid ◽  
Reduction Mechanisms ◽  
Internal Fluid Flow ◽  
Flow Induced Vibrations ◽  
Flow Variables

Internal fluid flow parameters in conjunction with elastomechanical properties of conveyance systems have significantly modulated flow induced vibrations in pipeline and riser systems. Recent advances on the mechanics of sandwich elastic systems as effective vibration and noise reduction mechanisms have simulated the possibility of replacing traditional steel pipes with sandwich pipes in deepwater environment. The dynamic behaviour and stability of sandwich elastic pipes conveying a non-Newtonian fluid are investigated in this paper. For this problem, a set of generalised non-linear equations governing the vibration of sandwich pipes held together in pressurised environment and conveying a non-Newtonian fluid is presented. By linearizing the governing partial differential equation matching the problem physics, under slight perturbation of the internal fluid velocity and other flow variables closed form analytical results for the system dual natural frequencies and stability under external excitation are computed for field designs and applications. Results show that for a given length of pipe, beyond the critical velocity, instability increases with the velocity of conveyance.

Fluid Pressures on Unanchored Rigid Flat-Bottom Cylindrical Tanks Under Action of Uplifting Acceleration

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Tomoyo Taniguchi ◽  
Yoshinori Ando
Keyword(s):  
Velocity Potential ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Angular Acceleration ◽  
Bottom Plate ◽  
Center Line ◽  
Cylindrical Tank ◽  
Cylindrical Coordinates ◽  
Flat Bottom ◽  
Cylindrical Tanks

To protect flat-bottom cylindrical tanks against severe damage from uplift motion, accurate evaluation of accompanying fluid pressures is indispensable. This paper presents a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank in the same manner as the procedure outlined and discussed previously by the authors (Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801). With perfect fluid and velocity potential assumed, the Laplace equation in cylindrical coordinates gives a continuity equation, while fluid velocity imparted by the displacement (and its time derivatives) of the shell and bottom plate of the tank defines boundary conditions. The velocity potential is solved with the Fourier–Bessel expansion, and its derivative, with respect to time, gives the fluid pressure at an arbitrary point inside the tank. In practice, designers have to calculate the fluid pressure on the tank whose perimeter of the bottom plate lifts off the ground like a crescent in plan view. However, the asymmetric boundary condition given by the fluid velocity imparted by the deformation of the crescent-like uplift region at the bottom cannot be expressed properly in cylindrical coordinates. This paper examines applicability of a slice model, which is a rigid rectangular tank with a unit depth vertically sliced out of a rigid flat-bottom cylindrical tank with a certain deviation from (in parallel to) the center line of the tank. A mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with Fourier series. It well converges with a few first terms of the Fourier series and accurately calculates the values of the fluid pressure on the tank. In addition, the slice model approximates well the values of the fluid pressure on the shell of a rigid flat-bottom cylindrical tank for any points deviated from the center line. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. The proposed mathematical and graphical methods are cost effective and aid in the design of the flat-bottom cylindrical tanks that allow the uplifting of the bottom plate.

BLOOD FLOW IN CORONARY ARTERY BIFURCATION CALCULATED BY TURBULENT FINITE ELEMENT MODEL

2021 ◽  
Author(s):  
Aleksandar Nikolić ◽  
◽  
Marko Topalović ◽  
Milan Blagojević ◽  
Vladimir Simić
Keyword(s):  
Finite Element ◽  
Blood Flow ◽  
Kinetic Energy ◽  
Finite Element Model ◽  
Fluid Velocity ◽  
Fluid Pressure ◽  
Element Model ◽  
Viscous Sublayer ◽  
Flow Problems ◽  
Analysis Of Results

Simulation of blood flow in this paper is analyzed using two-equation turbulent finite element model that can calculate values in the viscous sublayer. Implicit integration of the equations is used for determining the fluid velocity, fluid pressure, turbulence, kinetic energy, and dissipation of turbulent kinetic energy. These values are calculated in the finite element nodes for each step of incremental- iterative procedure. Developed turbulent finite element model, with the customized generation of finite element meshes, is used for calculating complex blood flow problems. Analysis of results showed that a cardiologist can use proposed tools and methods for investigating the hemodynamic conditions inside bifurcation of arteries.

scholarly journals Analytical solution of settling behavior of a particle in incompressible Newtonian fluid by using Parameterized Perturbation Method

2014 ◽  
Vol 33 (2) ◽  
pp. 145-160
Author(s):  
Reza Mohammadyari ◽  
Mazaher Rahimi Esboee ◽  
Majid Rahgoshay
Keyword(s):  
Perturbation Method ◽  
Newtonian Fluid ◽  
Mass Term ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Unsteady Motion ◽  
High Rate ◽  
Settling Behavior ◽  
Analytical Expressions ◽  
Parameterized Perturbation Method

The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM), analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.

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