scholarly journals Flow between caoxial rotating disks: with and without externally applied magnetic field

1981 ◽  
Vol 4 (1) ◽  
pp. 181-200 ◽  
Author(s):  
R. K. Bhatnagar
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Viscoelastic Fluid ◽  
Constant Angular Velocity ◽  
Linear Ordinary Differential Equation ◽  
The Other ◽  
Rotating Disks ◽  
Governing System ◽  
Angular Velocities

The problem of flow of a Rivlin-Ericksen type of viscoelastic fluid is discussed when such a fluid is confined between two infinite rotating coaxial disks. The governing system of a pair of non-linear ordinary differential equation is solved by treating Reynolds number to small. The three cases discussed are: (I) one disks is held at rest while other rotates with a constant angular velocity, (ii) one disk rorates faster than the other but in the same sense and (iii) the disks rotate in opposite senses and with different angular velocities. The radial, tranverse and axial components of the velocity field are plotted for the above three cases for different values of the Reynolds number. The results obtained for a viscoelastic fluid are compared with those for a Newtonian fluid. The velocity field for case (i) is also computed when a magnetic field is applied in a direction perpendicular to the discs and the results are compared with the case when magnetic field is absent. Some interesting features are observed for a viscoelastic fluid.

Computation of the flow between two rotating coaxial disks: multiplicity of steady-state solutions

1981 ◽  
Vol 108 ◽  
pp. 227-240 ◽  
Author(s):  
M. Holodniok ◽  
M. Kubí[cscr ]ek ◽  
V. Hlavá[cscr ]ek
Keyword(s):  
Reynolds Number ◽  
Steady State ◽  
Detailed Comparison ◽  
Continuation Methods ◽  
Rotating Disks ◽  
Angular Velocities ◽  
Newton Raphson ◽  
Grid Points ◽  
Steady State Solutions ◽  
Number Of Branches

A numerical investigation of the problem of rotating disks is made using the Newton-Raphson and continuation methods. The numerical analysis of the problem was performed for a sequence of values of the Reynolds number R and the ratio of angular velocities of both disks s. It was shown that for higher values of the Reynolds number it is necessary to use a large number of grid points. Continuation of the solution with respect to the parameter s indicated that a number of branches may exist. A detailed discussion for three selected values of s (s = -1, s = 0, s = 1) is presented together with a detailed comparison of our calculations with results already published in the literature.

Fluctuating Flow of a Viscoelastic Fluid in a Porous Channel

1979 ◽  
Vol 46 (1) ◽  
pp. 21-25 ◽  
Author(s):  
R. K. Bhatnagar
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Mass Flux ◽  
Constant Velocity ◽  
Frequency Parameter ◽  
Viscous Fluids ◽  
The Other ◽  
Phase Lag ◽  
Viscoelastic Parameter ◽  
Viscosity Parameter

The problem of flow of a viscoelastic fluid characterized by the well-known Rivlin-Ericksen constitutive equations is discussed, when such a fluid is driven by an unsteady pressure gradient in the region between two parallel porous plates. It is assumed that on one plate the fluid is injected with certain constant velocity and that it is sucked off at the other with the same velocity. The governing differential equations, which do not involve the cross-viscosity parameter, are solved using a pertubation scheme treating the viscoelastic parameter to be small. The behavior of instantaneous velocity profiles, and magnitude and the phase lag of mass flux, which depend on the injection Reynolds number, the frequency parameter, and the viscoelastic parameter are discussed for various values of these parameters. Some very interesting departures of these from the corresponding flow of classical viscous fluids are reported when one or both of the injection Reynolds number and frequency parameter are small or large.

The magnetohydrodynamic flow past a flat plate

1959 ◽  
Vol 6 (1) ◽  
pp. 77-96 ◽  
Author(s):  
H. P. Greenspan ◽  
G. F. Carrier
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Flat Plate ◽  
Steady Flow ◽  
Full Range ◽  
Ambient Magnetic Field ◽  
Electrically Conducting ◽  
Electrically Conducting Fluid ◽  
Two Parameters

The uniform steady flow of an incompressible, viscous, electrically conducting fluid is distorted by the presence of a symmetrically oriented semi-infinite flat plate. The ambient magnetic field is coincident with the ambient velocity field. The description of the resulting fields depends on the physical co-ordinates measured in units of Reynolds number and on the two parameters ε = ωμν and β = μH2/ρv2. This description of the fields is approximated in three different ways and essentially covers the full range of ε and β. In particular, when β [Gt ] 1, no steady flow which is uniform at large distances from the plate exists.

scholarly journals Comparison of Micro-Mixing in Time Pulsed Newtonian Fluid and Viscoelastic Fluid

Micromachines ◽  
2019 ◽  
Vol 10 (4) ◽  
pp. 262 ◽  
Author(s):  
Zhang ◽  
Zhang ◽  
Wu ◽  
Shen ◽  
Chen ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Newtonian Fluid ◽  
Viscoelastic Fluid ◽  
Flow Rate ◽  
Essential Role ◽  
Weissenberg Number ◽  
The Other ◽  
Fluid Mixing ◽  
Constant Flow ◽  
Constant Flow Rate

Fluid mixing plays an essential role in many microfluidic applications. Here, we compare the mixing in time pulsing flows for both a Newtonian fluid and a viscoelastic fluid at different pulsing frequencies. In general, the mixing degree in the viscoelastic fluid is higher than that in the Newtonian fluid. Particularly, the mixing in Newtonian fluid with time pulsing is decreased when the Reynolds number Re is between 0.002 and 0.01, while it is enhanced when Re is between 0.1 and 0.2 compared with that at a constant flow rate. In the viscoelastic fluid, on the other hand, the time pulsing does not change the mixing degree when the Weissenberg number Wi ≤ 20, while a larger mixing degree is realized at a higher pulsing frequency when Wi = 50.

On Oseen's approximation

1962 ◽  
Vol 13 (4) ◽  
pp. 557-569 ◽  
Author(s):  
W. Chester
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Stokes Equations ◽  
Absolute Magnitude ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
First Order ◽  
Hydrodynamic Effects

An investigation is made into the validity of the Oseen equations, for incom-pressible, viscous flow past a body, as an approximation to the Navier-Stokes equations. It is shown that, when the body is such that a reversal of the uniform flow at infinity merely reverses any component of the force on the body without changing its absolute magnitude, that component can be determined correctly to the first order in the Reynolds number, though the detailed velocity field is not correct to this order. Moreover, this force can be deduced simply from a knowledge of the force on the body according to Stokes's approximation.The analysis is also generalized to include the magneto-hydrodynamic effects when the fluid is conducting and the flow takes place in the presence of a magnetic field.

Research on Velocity and Inducted Magnetic Field of Conducting Flow in 2D

2013 ◽  
Vol 432 ◽  
pp. 163-167
Author(s):  
Yang Liu ◽  
Ya Ge You ◽  
Ya Qun Zhang ◽  
Xue Ling Cao
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Velocity Field ◽  
Exact Solutions ◽  
Steady Flow ◽  
Magnetic Reynolds Number ◽  
The Magnetic Field

The purpose of this paper is to present the results of velocity and inducted magnetic field based on thedimensionlessgoverning equations of the incompressible, viscous, instant fluid from equation (1) to equation (6).We assumed a full developed and steady flow so that we can get the exact solutions. Firstly, we considered the situation of low magnetic Reynolds number and inducted magnetic field being ignored. Then secondly, we considered the situation of large magnetic Reynolds number. By comparing these two situations, we found two results: (1). theelectromagnetic force produced by the magnetic field changes the original velocity field a lot (Fig.2 and Fig.3); (2). the inducted magnetic field decreases with the decrease of magnetic Reynolds number. The results also prove that the inducted magnetic field can be ignored when the magnetic Reynolds number is less than or equal to 1 (Fig.5).

A Similar Flow Between Two Rotating Disks in the Presence of a Magnetic Field

1993 ◽  
Vol 60 (3) ◽  
pp. 707-714 ◽  
Author(s):  
R. Usha ◽  
S. Vasudevan
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Magnetic Force ◽  
Considerable Increase ◽  
Analytic Solutions ◽  
Nonlinear Ordinary Differential Equations ◽  
Rotating Disks ◽  
Normal Forces ◽  
Magnetic Forces ◽  
Parallel Disks

A similarity solution is obtained for a flow between two rotating parallel disks which, at time t* are spaced a distance H (1 − αt*)1/2 apart and a magnetic field proportional to B0(1 − αt*)−1/2 is applied perpendicular to the disks. Approximate analytic solutions are given and a numerical solution to the resulting nonlinear ordinary differential equations is presented. The effects of magnetic forces on the velocity profiles, the normal forces and the torques which the fluid exerts on the disks are studied. It is observed that by increasing the magnetic force a considerable increase in the load can be achieved. Also, the torques are more sensitive to changes in the squeeze Reynolds number than to changes in the rotation Reynolds number.

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

Modeling mass transfer and substrate utilization in the boundary layer of biofilm systems

1998 ◽  
Vol 37 (4-5) ◽  
pp. 139-147 ◽  
Author(s):  
Harald Horn ◽  
Dietmar C. Hempel
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Reynolds Number ◽  
Film Theory ◽  
Substrate Utilization ◽  
The Other ◽  
Concentration Profiles ◽  
Hydrodynamic Conditions ◽  
Time Axis ◽  
Transfer Coefficients

The use of microelectrodes in biofilm research allows a better understanding of intrinsic biofilm processes. Little is known about mass transfer and substrate utilization in the boundary layer of biofilm systems. One possible description of mass transfer can be obtained by mass transfer coefficients, both on the basis of the stagnant film theory or with the Sherwood number. This approach is rather formal and not quite correct when the heterogeneity of the biofilm surface structure is taken into account. It could be shown that substrate loading is a major factor in the description of the development of the density. On the other hand, the time axis is an important factor which has to be considered when concentration profiles in biofilm systems are discussed. Finally, hydrodynamic conditions become important for the development of the biofilm surface when the Reynolds number increases above the range of 3000-4000.

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