Magnetohydrodynamic Generalized Couette Flow (With Uniform Suction; Time-Dependent Pressure Gradient; and Arbitrary Initial Velocity)

1970 ◽  
Vol 37 (4) ◽  
pp. 1189-1190 ◽  
Author(s):  
Y. D. Wadhwa
Keyword(s):  
Pressure Gradient ◽  
Couette Flow ◽  
Initial Velocity ◽  
Time Dependent ◽  
Uniform Suction

Couette Flow of a Generalized Oldroyd-B Fluid due to Constantly Accelerated Shear Stress Coupled with the Pressure Gradient

2011 ◽  
Vol 354-355 ◽  
pp. 179-182
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Jia Jia Niu
Keyword(s):  
Shear Stress ◽  
Laplace Transform ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Hankel Transform ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Finite Hankel Transform

This paper presented an analysis for the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress with the influence of the internal constantly decelerated pressure gradient. The exact solutions are established by means of the combine of the sequential fractional derivatives Laplace transform and finite Hankel transform and presented by integral and series form in terms of the Mittag-Leffler function. Moreover, the effects of various parameters are analyzed in detail by graphical illustrations.

Exact Solutions for the Fractional Time-Dependent Oldroyd-B Fluid Model Subject to a Constantly Accelerated Shear Stress

2014 ◽  
Vol 518 ◽  
pp. 114-119 ◽  
Author(s):  
Chun Rui Li ◽  
Lian Cun Zheng
Keyword(s):  
Shear Stress ◽  
Velocity Field ◽  
Pressure Gradient ◽  
Exact Solutions ◽  
Couette Flow ◽  
Fractional Derivatives ◽  
Fluid Model ◽  
Time Dependent ◽  
Infinite Cylinder ◽  
Model Subject

In this paper, based on the fractional model, we present an investigation on the couette flow of a generalized Oldroyd-B fluid within an infinite cylinder subject to a time-dependent shear stress which is affected by the internal constantly decelerated pressure gradient. By using the fractional derivatives Laplace and finite Hankel transforms, the obtained solutions for the velocity field and shear stress, written in terms of generalized R function, are presented the similar characteristics with Newtonian and non-Newtonian fluids. Moreover, the effects of various parameters are systematically analyzed.

scholarly journals ANALYTICAL SOLUTION FOR TRANSIENT ONEDIMENSIONAL COUETTE FLOW CONSIDERING CONSTANT AND TIME-DEPENDENT PRESSURE GRADIENTS

2009 ◽  
Vol 8 (2) ◽  
pp. 92 ◽  
Author(s):  
A. A. Mendiburu ◽  
L. R. Carrocci ◽  
J. A. Carvalho
Keyword(s):  
Pressure Gradient ◽  
Couette Flow ◽  
Stokes Equations ◽  
Transient State ◽  
Integral Transforms ◽  
Time Dependent ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Navier Stokes Equations ◽  
The One

This paperaims to determine the velocity profile, in transient state, for a parallel incompressible flow known as Couette flow. The Navier-Stokes equations were applied upon this flow. Analytical solutions, based in Fourier series and integral transforms, were obtained for the one-dimensional transient Couette flow, taking into account constant and time-dependent pressure gradients acting on the fluid since the same instant when the plate starts it´s movement. Taking advantage of the orthogonality and superposition properties solutions were foundfor both considered cases. Considering a time-dependent pressure gradient, it was found a general solution for the Couette flow for a particular time function. It was found that the solution for a time-dependent pressure gradient includes the solutions for a zero pressure gradient and for a constant pressure gradient.

Unsteady MHD Couette Flow and Heat Transfer Between Parallel Porous Plates With Exponential Decaying Pressure Gradient

2005 ◽  
Author(s):  
Hazem A. Attia
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Pressure Gradient ◽  
Couette Flow ◽  
Fluid Motion ◽  
Electrically Conducting ◽  
Uniform Suction ◽  
Flow And Heat Transfer ◽  
Unsteady Couette Flow ◽  
Mhd Couette Flow

The unsteady Couette flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel non-conducting porous plates is studied with heat transfer. An external uniform magnetic field and a uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are included in the energy equation. The effect of the magnetic field and the uniform suction and injection on both the velocity and temperature distributions is examined.

scholarly journals Effect of an oscillating time-dependent pressure gradient on Dean flow: transient solution

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Basant K. Jha ◽  
Dauda Gambo
Keyword(s):  
Pressure Gradient ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Outer Cylinder ◽  
Time Dependent ◽  
Navier Stokes ◽  
Dean Flow ◽  
Continuity Equations ◽  
Riemann Sum ◽  
Flow Formation

Abstract Background Navier-Stokes and continuity equations are utilized to simulate fully developed laminar Dean flow with an oscillating time-dependent pressure gradient. These equations are solved analytically with the appropriate boundary and initial conditions in terms of Laplace domain and inverted to time domain using a numerical inversion technique known as Riemann-Sum Approximation (RSA). The flow is assumed to be triggered by the applied circumferential pressure gradient (azimuthal pressure gradient) and the oscillating time-dependent pressure gradient. The influence of the various flow parameters on the flow formation are depicted graphically. Comparisons with previously established result has been made as a limit case when the frequency of the oscillation is taken as 0 (ω = 0). Results It was revealed that maintaining the frequency of oscillation, the velocity and skin frictions can be made increasing functions of time. An increasing frequency of the oscillating time-dependent pressure gradient and relatively a small amount of time is desirable for a decreasing velocity and skin frictions. The fluid vorticity decreases with further distance towards the outer cylinder as time passes. Conclusion Findings confirm that increasing the frequency of oscillation weakens the fluid velocity and the drag on both walls of the cylinders.

Tertiary solutions and their stability in rotating plane Couette flow

1998 ◽  
Vol 358 ◽  
pp. 357-378 ◽  
Author(s):  
M. NAGATA
Keyword(s):  
Reynolds Number ◽  
Couette Flow ◽  
Stability Boundary ◽  
Streamwise Vortex ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Plane Couette Flow ◽  
Streamwise Direction ◽  
The Stability ◽  
Oscillatory Instabilities

The stability of nonlinear tertiary solutions in rotating plane Couette flow is examined numerically. It is found that the tertiary flows, which bifurcate from two-dimensional streamwise vortex flows, are stable within a certain range of the rotation rate when the Reynolds number is relatively small. The stability boundary is determined by perturbations which are subharmonic in the streamwise direction. As the Reynolds number is increased, the rotation range for the stable tertiary motions is destroyed gradually by oscillatory instabilities. We expect that the tertiary flow is overtaken by time-dependent motions for large Reynolds numbers. The results are compared with the recent experimental observation by Tillmark & Alfredsson (1996).

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