An Exact Periodic Solution of a Hydromagnetic Flow of an Oldroyd Fluid in a Channel

1999 ◽  
Vol 66 (4) ◽  
pp. 974-977 ◽  
Author(s):  
R. N. Ray ◽  
A. Samad ◽  
T. K. Chaudhury
Keyword(s):  
Periodic Solution ◽  
Unsteady Flow ◽  
Velocity Gradient ◽  
Separation Of Variables ◽  
The Other ◽  
Parallel Plates ◽  
Hydromagnetic Flow ◽  
Mean Velocity ◽  
Oldroyd Fluid ◽  
Viscoelastic Parameters

The unsteady flow of a conducting Oldroyd fluid between two parallel plates, one of which is at rest and the other oscillating in its own plane with a constant mean velocity, has been investigated. Using separation of variables an exact periodic solution for the problem is obtained. Effects of viscoelastic parameters on velocity gradient, skin friction amplitude, and phase angle of the flow are discussed with graphs.

An Exact Periodic Solution of a Hydromagnetic Flow in a Horizontal Channel

1988 ◽  
Vol 55 (4) ◽  
pp. 981-983 ◽  
Author(s):  
K. Vajravelu
Keyword(s):  
Exact Solution ◽  
Periodic Solution ◽  
Flow Field ◽  
Unsteady Flow ◽  
Incompressible Fluid ◽  
Approximate Solutions ◽  
The Other ◽  
Hydromagnetic Flow ◽  
Mean Velocity ◽  
Approximate Form

An exact periodic solution for the hydromagnetic unsteady flow of an incompressible fluid with constant properties is obtained. The hydrodynamic (HD) and the hydromagnetic (HM) cases are studied. The flow field here is a generalization of the well-known Couette flow, in which one wall is at rest and the other wall oscillates in its own plane about a constant mean velocity. In order to have some suggestions about the approximate solutions, the exact solution is compared with its own approximate form.

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

scholarly journals Solution of the Graetz–Nusselt Problem for Liquid Flow Over Isothermal Parallel Ridges

2017 ◽  
Vol 139 (9) ◽  
Author(s):  
Georgios Karamanis ◽  
Marc Hodes ◽  
Toby Kirk ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Boundary Condition ◽  
Temperature Profile ◽  
Mixed Boundary ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
The Other ◽  
Inlet Temperature ◽  
Textured Surface ◽  
Parallel Plates ◽  
Time Required

We consider convective heat transfer for laminar flow of liquid between parallel plates that are textured with isothermal ridges oriented parallel to the flow. Three different flow configurations are analyzed: one plate textured and the other one smooth; both plates textured and the ridges aligned; and both plates textured, but the ridges staggered by half a pitch. The liquid is assumed to be in the Cassie state on the textured surface(s), to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. Heat is exchanged with the liquid either through the ridges of one plate with the other plate adiabatic, or through the ridges of both plates. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). Axial conduction is neglected and the inlet temperature profile is arbitrary. We solve for the three-dimensional developing temperature profile assuming a hydrodynamically developed flow, i.e., we consider the Graetz–Nusselt problem. Using the method of separation of variables, the thermal problem is essentially reduced to a two-dimensional eigenvalue problem in the transverse coordinates, which is solved numerically. Expressions for the local Nusselt number and those averaged over the period of the ridges in the developing and fully developed regions are provided. Nusselt numbers averaged over the period and length of the domain are also provided. Our approach enables the aforementioned quantities to be computed in a small fraction of the time required by a general computational fluid dynamics (CFD) solver.

The Estimation of Discharge in an Experimental Open Channel

2014 ◽  
Vol 905 ◽  
pp. 369-373
Author(s):  
Choo Tai Ho ◽  
Yoon Hyeon Cheol ◽  
Yun Gwan Seon ◽  
Noh Hyun Suk ◽  
Bae Chang Yeon
Keyword(s):  
Unsteady Flow ◽  
River Discharge ◽  
Open Channel ◽  
Flow Conditions ◽  
Mean Velocity ◽  
Velocity Equation ◽  
The Mean ◽  
Loop Form

The estimation of a river discharge by using a mean velocity equation is very convenient and rational. Nevertheless, a research on an equation calculating a mean velocity in a river was not entirely satisfactory after the development of Chezy and Mannings formulas which are uniform equations. In this paper, accordingly, the mean velocity in unsteady flow conditions which are shown loop form properties was estimated by using a new mean velocity formula derived from Chius 2-D velocity formula. The results showed that the proposed method was more accurate in estimating discharge, when compared with the conventional formulas.

scholarly journals Unsteady flow induced by a withdrawal point beneath a free surface

2005 ◽  
Vol 47 (2) ◽  
pp. 185-202 ◽  
Author(s):  
T. E. Stokes ◽  
G. C. Hocking ◽  
L. K. Forbes
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Unsteady Flow ◽  
Critical Values ◽  
The Other ◽  
Withdrawal Rate ◽  
Steady Solutions

AbstractThe unsteady axisymmetric withdrawal from a fluid with a free surface through a point sink is considered. Results both with and without surface tension are included and placed in context with previous work. The results indicate that there are two critical values of withdrawal rate at which the surface is drawn directly into the outlet, one after flow initiation and the other after the flow has been established. It is shown that the larger of these values corresponds to the point at which steady solutions no longer exist.

scholarly journals Resolved Gas Kinematics in a Sample of Low-Redshift High Star-Formation Rate Galaxies

2016 ◽  
Vol 33 ◽  
Author(s):  
Mathew Varidel ◽  
Michael Pracy ◽  
Scott Croom ◽  
Matt S. Owers ◽  
Elaine Sadler
Keyword(s):  
Star Formation ◽  
Velocity Gradient ◽  
Velocity Dispersion ◽  
Star Formation Rate ◽  
Formation Rate ◽  
Local Effect ◽  
Line Of Sight ◽  
Mean Velocity ◽  
Gas Kinematics ◽  
Integral Field Spectroscopy

AbstractWe have used integral field spectroscopy of a sample of six nearby (z ~ 0.01–0.04) high star-formation rate ($\text{SFR} \sim 10\hbox{--}40$$\text{M}_\odot \text{ yr$^{-1}$}$) galaxies to investigate the relationship between local velocity dispersion and star-formation rate on sub-galactic scales. The low-redshift mitigates, to some extent, the effect of beam smearing which artificially inflates the measured dispersion as it combines regions with different line-of-sight velocities into a single spatial pixel. We compare the parametric maps of the velocity dispersion with the Hα flux (a proxy for local star-formation rate), and the velocity gradient (a proxy for the local effect of beam smearing). We find, even for these very nearby galaxies, the Hα velocity dispersion correlates more strongly with velocity gradient than with Hα flux—implying that beam smearing is still having a significant effect on the velocity dispersion measurements. We obtain a first-order non parametric correction for the unweighted and flux weighted mean velocity dispersion by fitting a 2D linear regression model to the spaxel-by-spaxel data where the velocity gradient and the Hα flux are the independent variables and the velocity dispersion is the dependent variable; and then extrapolating to zero velocity gradient. The corrected velocity dispersions are a factor of ~ 1.3–4.5 and ~ 1.3–2.7 lower than the uncorrected flux-weighted and unweighted mean line-of-sight velocity dispersion values, respectively. These corrections are larger than has been previously cited using disc models of the velocity and velocity dispersion field to correct for beam smearing. The corrected flux-weighted velocity dispersion values are σm ~ 20–50 km s−1.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

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