Flow Of Viscous Incompressible Fluid Research Articles

A Note on the Temperature Distribution in a Porous Annulus

Unsteady temperature distribution for flow of an incompressible viscous fluid in a porous annulus has been investigated under the assumption that the rate of injection of the fluid at the inner cylinder is equal to the rate of suction of the fluid at the outer one. Viscous dissipation has been neglected while rate of heat generation in the fluid has been accounted for. An expression for the temperature distribution has been obtained using Laplace transform technique and taking the temperatures of the boundaries to be functions of time.

Dusty Viscous Flow Through The Annulus Between two Coaxial Circular Cylinders

Unsteady laminar flow of a dusty viscous incompressible fluid through the annular tube formed by two coaxial circular cylinders is discussed under two situation : (i) when the pressure gradient varies harmonically with time: and (ii) when there is an exponential pressure gradient. The flow through a circular pipe is obtained as a particular case, making the radius of the inner cylinder tend to zero.

Note on evolutionary free piston problem for Stokes equations with slip boundary conditions

In this paper we study a free boundary fluid-rigid body interaction problem, the free piston problem.We consider an evolutionary incompressible viscous fluid flow through a junction of two pipes. Insidethe 'vertical' pipe there is a heavy piston which can freely slide along the pipe. On the lateralboundary of the 'vertical' pipe we prescribe Navier's slip boundary conditions. We prove the existence ofa local in time weak solution. Furthermore, we show that the obtained solution is a strong solution.

On a linearized system arising in the study of viscous surface flow down an inclined plane

We consider the linearized problem describing motion of a viscous incompressible fluid flow down an inclined plane under the effect of gravity. We formulate the problem for downward periodic disturbances from the laminar steady flow as an evolution equation in the product of Sobolev spaces \(H^{\frac{3}{2}}_0({\mathbb {T}}) \times {\mathbb {P}}^0H^0(\Omega ) \). It is crucial to study qualitative behavior of solutions that the operator arising in the linearized problem has compact resolvent operators and generates an analytic semigroup in \(H^{\frac{3}{2}}_0({\mathbb {T}}) \times {\mathbb {P}}^0H^0(\Omega ) \).

Unsteady Flow and Heat Transfer in a Viscous Incompressible Fluid due to the Oscillations of a Porous Cylinder with Suction

Navier-Stokes equations which described the unsteady flow of viscous incompressible fluid a around a porous infinite circular cylinder oscillating harmonically with constant suction are integrated using Laplace transform. Curves have been drawn of the steady state part of the velocity both for suction and without suction case and it is found that for each value of suction parameter a situation which does not exist in the case of rotating cylinder. The energy equation has also been solved and the solutions are given for large and small values of time.

Hall Effects on Unsteady MHD Three Dimensional Flow through a Porous Medium in a Rotating Parallel Plate Channel with Effect of Inclined Magnetic Field

In this paper, we make an initial value investigation of the unsteady flow of incompressible viscous fluid between two rigid non-conducting rotating parallel plates bounded by a porous medium under the influence of a uniform magnetic field of strength H0 inclined at an angle of inclination α with normal to the boundaries taking hall current into account. The perturbations are created by a constant pressure gradient along the plates in addition to the non-torsional oscillations of the upper plate while the lower plate is at rest. The flow in the porous medium is governed by the Brinkman’s equations. The exact solution of the velocity in the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated in detail and the ultimate quasi-steady state solution has been derived analytically. Its behaviour is computationally discussed with reference to the various governing parameters. The shear stresses on the boundaries are also obtained analytically and their behaviour is computationally discussed.

Thin helical vortex dynamics in low-viscosity liquid

The problem of helical vortices description has the significant interest as from fundamental point of view as well for practice. In some sense this problem is close to the vortex ring one which attracted much more attention in last decades. The reviews on the vortex rings investigations can be found in recent papers (1, 2) or in book by Akhmetov (3). In particular, in series of papers by Kaplanskii with co-authors (4-6) there was considered the viscosity influence on the vortex ring evolution. Separate attention was paid to the low Reynolds number case and to high Reynolds number one, initial stage of viscous evolution and final one. This paper presents first attempt for research on the diffusion and dynamics of a viscous helical vortex. In this work the problem of thin helical dynamics in low-viscosity liquid is considered. Appearance of helical vortex in the flow assumes helical symmetry. It means, that all of flow characteristic will be constant along the helical lines. The flow of viscous incompressible fluid under condition of the helical symmetry is described in variables vorticity - stream function by the system of equations (7, 8) 2

Viscous Dissipation Effect on Natural Convection Flow along a Vertical Wavy Surface

This paper investigates the influence of viscous dissipation on natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface. The governing boundary layer equations are transformed into dimensionless non-similar equations by using set of suitable transformations and solved numerically by the finite difference method along with Newton's linearization approximation. Results for the details of the surface shear stress in terms of the local skin friction coefficient, the rate of heat transfer in terms of the local Nusselt number, the streamlines and the isotherms are shown graphically in figures along the wavy surface for different values of the set of parameters entering into the problem. It is observed that the viscous dissipation parameter N and amplitude-to-length ratio of wavy surface α have accelerating effect on the velocity and temperature of the flow field. Both N and α retards the heat transfer rate. The effect of viscous dissipation parameter N is to enhance the skin friction coefficient while amplitude-to-length ratio of wavy surface α reverses the effect.

Combined Effects of Centrifugal and Coriolis Instability of the Flow Through a Rotating Curved Duct of Small Curvature

In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct of small curvature. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Taylor number 0≤Tr≤2000 for the Dean numbers Dn=500 and 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr=100, where the outer wall is heated and the inner wall cooled. The rotation of the duct about the center of curvature is imposed, and the effects of rotation (Coriolis force) on the unsteady flow characteristics are investigated. It is found that the unsteady flow undergoes in the scenario ‘Chaotic→ multi-periodic→ periodic → steady-state’, if Tr is increased in the positive direction. Contours of secondary flow patterns and temperature profiles are also obtained at several values of Tr, and it is found that there exist two- and multi-vortex solutions for the unsteady flow if the duct rotation is involved in the present cases.

MHD Natural Convection with Convective Surface Boundary Condition over a Flat Plate

We apply the one parameter continuous group method to investigate similarity solutions of magnetohydrodynamic (MHD) heat and mass transfer flow of a steady viscous incompressible fluid over a flat plate. By using the one parameter group method, similarity transformations and corresponding similarity representations are presented. A convective boundary condition is applied instead of the usual boundary conditions of constant surface temperature or constant heat flux. In addition it is assumed that viscosity, thermal conductivity, and concentration diffusivity vary linearly. Our study indicates that a similarity solution is possible if the convective heat transfer related to the hot fluid on the lower surface of the plate is directly proportional to(x-)-1/2wherex-is the distance from the leading edge of the solid surface. Numerical solutions of the ordinary differential equations are obtained by the Keller Box method for different values of the controlling parameters associated with the problem.

Magnetic field effect on fluid flow through a rotating rectangular straight duct with large aspect ratio

Numerical study has been performed to investigate the fluid flow through a rotating rectangular straight duct in the presence of magnetic field under various flow conditions. Spectral method is applied as a main tool for the numerical calculation technique, where the Chebyshev polynomial, collocation method and the Newton-Raphson method are also used as secondary tools. The magnetohydrodynamic incompressible viscous steady fluid flow through a straight duct of rectangular cross-section rotating at a constant angular velocity about the centre of the duct cross-section is investigated to examine the combined effects of magnetic parameter ( M g ), rotational parameter ( T r ), pressure driven parameter ( D n ) and aspect ratio (γ). One of the interesting phenomena of the flow is the solution curve and the flow structure. The flow structures in case of rotation of the duct axis, the pressure driven parameters with large magnetic parameters well as large rotational parameters are examined while other parameters remain constant. The calculations are carried out for 5 ≤ M g ≤ 50,000, 50 ≤ T r ≤ 100,000, D n = 500, 1,000, 1,500 and 2,000 where the aspect ratio 3.0.

RETRACTED: Higher-order Spectral/hp Finite Element Technology for Shells and Flows of Viscous Incompressible Fluids

This study deals with the use of high-order spectral/hp approximation functions in finite element models of various of nonlinear boundary-value and initial-value problems arising in the fields of structural mechanics and flows of viscous incompressible fluids. [...]

MICROPOLAR FLUID MODEL FOR BLOOD FLOW THROUGH A STENOSED ARTERY

Various experimental observations have demonstrated that the classical fluid theory is incapable of explaining many phenomena at micro and nano scales. On the other hand, micropolar fluid dynamics can naturally pick up the physical phenomena at these scales owing to its additional degrees of freedom caused by incorporating the effects of fluid molecules on the continuum. Therefore, one of the aims of this paper is to investigate the applicability of the theory of micropolar fluids to modeling and calculating flows in circular microchannels depending on the geometrical dimension of the flow field. Hence, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, the analytical and exact solution of the micropolar Hagen–Poiseuille flow in a circular microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is also shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow such as blood flow in a stenosed artery, having multiple kinds of stenoses, is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

FINITE ELEMENT SIMULATION OF MICROPOLAR FLUID FLOW IN THE LID-DRIVEN SQUARE CAVITY

The micropolar fluid theory augments the laws of classical continuum mechanics by incorporating the effects of fluid molecules on the continuum. So, the micropolar theory has been able to explain many phenomena at micro and nano scales. In this paper, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, analytical solution of the Poiseuille flow of micropolar fluid in a microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow in a lid-driven square cavity is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

Numerical Study of the RespiCon Sampler Performance in the Calm Air

Results of a numerical study of the RespiCon sampler performance in the calm air are presented. The air flow is described by the Navier–Stokes equations of axisymmetric stationary viscous flow of incompressible fluid that are numerically integrated by the computational fluid dynamics (CFD) software FLUENT. The collection efficiencies of RespiCon impactor stages agree quite well with experimental data and curves of the European standards for the thoracic and respirable dust fractions. The aspiration efficiencies derived from the numerical model overestimate the experimental data in the range of particle sizes of 10 μm < dp < 40 μm; however, they correctly predict the value of maximal size of aspirated particles. A new design of the RespiCon sampler with a higher volume flow rate was developed. Copyright 2014 American Association for Aerosol Research

A note on regularity and uniqueness of natural convection with effects of viscous dissipation in 3D open channels

We prove the existence of unique regular solutions of steady-state buoyancy-driven flows of viscous incompressible heat-conducting fluids in 3D open channels under mixed boundary conditions. The model takes into account the phenomena of the viscous energy dissipation.

Incompressible Viscoelastic Flow of a Generalised Oldroyed-B Fluid through Porous Medium between Two Infinite Parallel Plates in a Rotating System

ABSTRACT Incompressible viscous fluid flow through a porous medium between two infinite parallel plates with moving upper plate in a rotating system has been studied here. The exact solution of the governing equation for the velocity field has been obtained by using Laplace and finite Fourier sine transformations in series form in terms of Mittage-Leffler function. It can be found that the fluid velocity decreases with the increasing values of fractional calculus parameter α and the permeability of the porous medium K. It can be also observed that the fluid velocity increases with the higher values of the viscosity of the porous medium. The dependence of the velocity field on fractional calculus parameters as well as material parameters has been illustrated graphically. Keywords Caputo operator; Generalised Oldroyed-B fluid; Laplace transformation: Finite Fourier sine transformation; porous medium . 1. INTRODUCTION In fluid dynamics the study of non-Newtonian fluid flow through porous medium has applications in different fields such as purification of crude oil, petroleum industry, polymer technology, electrostatic precipitation, irrigation, sanitary engineering, food industry etc. The flow behavior of non-Newtonian fluids cannot be described by Newtonian fluid model. For this reason various types of constitutive equations have been proposed and Oldroyed-B fluid model is one of them that has some success in describing non-Newtonian fluids. In recent years fractional calculus approach is found to be quite flexible in describing the viscoelastic fluids. In the approach the time derivative of integer order in the constitutive equation is replaced by Caputo fractional calculus operator. Charyulu and Ram [1] have investigated laminar flow of an incompressible micro polar fluid between two parallel plates with porous lining. Fetecau

Numerical Method in Two Dimensional Boundary Layer Theory for Incompressible Viscous Fluid

In this paper laminar flow of incompressible viscous fluid has been considered. Here two numerical methods for solving boundary layer equation have been discussed; (i) Keller Box scheme, (ii) Shooting Method. In Shooting Method, the boundary value problem has been converted into an equivalent initial value problem. Finally the Runge-Kutta method is used to solve the initial value problem. DOI: http://dx.doi.org/10.3329/rujs.v38i0.16549 Rajshahi University J. of Sci. 38, 61-73 (2010)

Two-layer flow of magnetic fluids

The plane two-layer flow of viscous incompressible fluids with differentmagnetic properties between two horizontal rigid planes in a nonuniform traveling magnetic field is investigated. An arbitrary nonuniform periodic traveling magnetic field generates wavelike changes in the interface between the media and fluid flows with nonzero flow rates. From the given magnetic field the interface shape and the velocities, pressures and mean flow rates of the fluids are calculated. The cases of a cosine magnetic force and of the magnetic field created by ferromagnetic cylinders moving in a uniform magnetic field are considered. The effect of various parameters on the mean flow rates of the fluids is investigated.

A space–time variational approach to hydrodynamic stability theory

We present a hydrodynamic stability theory for incompressible viscous fluid flows based on a space–time variational formulation and associated generalized singular value decomposition of the (linearized) Navier–Stokes equations. We first introduce a linear framework applicable to a wide variety of stationary- or time-dependent base flows: we consider arbitrary disturbances in both the initial condition and the dynamics measured in a ‘data’ space–time norm; the theory provides a rigorous, sharp (realizable) and efficiently computed bound for the velocity perturbation measured in a ‘solution’ space–time norm. We next present a generalization of the linear framework in which the disturbances and perturbation are now measured in respective selected space–time semi-norms ; the semi-norm theory permits rigorous and sharp quantification of, for example, the growth of initial disturbances or functional outputs. We then develop a (Brezzi–Rappaz–Raviart) nonlinear theory which provides, for disturbances which satisfy a certain (rather stringent) amplitude condition, rigorous finite-amplitude bounds for the velocity and output perturbations. Finally, we demonstrate the application of our linear and nonlinear hydrodynamic stability theory to unsteady moderate Reynolds number flow in an eddy-promoter channel.