Plane Couette flow

Velocity profiles of Plane Couette flow — Continuum - - - First-otder slip Boltzmann Eq... 

Fig. 4—Comparison of velocity profiles of plane Couette flow between different models.

It should be pointed out that the flow rate in the case of the Couette flow is independent of the inverse Knudsen number, and is the same as the prediction of the continuum model, although the velocity profiles predicted by the different flow models are different as shown in Fig. 4. The flow velocity in the case of the plane Couette flow is given as follows (i) Continuum model ... 

Figure 3. Finite element simulation of plane Couette flow with thermal dissipation and conductive heat transfer. (f) — fixed temperature condition (c) — convective boundary condition.

The nonequilibrium MD method we employed ( ) is the reservoir method (iff.) which simulates plane Couette flow. The effective viscosity Is calculated from the constitutive relation... 

The simulation value for the effective viscosity Is almost half the viscosity of the bulk fluid. According to the LADM the effective viscosity for plane Couette flow can be Identified as... 

Figure 4.2. The plane Couette flow. Reprinted with permission from Elsevier, Y. Demirel, Int. J. Heat Mass Transfer, 43 (2000) 4205.

Figure 4.4. Dimensionless temperature profile 0 for the plane Couette flow for v, = 5.0 m/s and H= 0.005 m. Reprinted with permission...

Lundbladh, A. and Johansson, A.V. (1991). Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech, 229, 499-576. 

Renardy and Renardy [66,73] have investigated the stability of plane Couette flows for Maxwell-type models involving the derivative (2). The flow lies between parallel plates at a = 0 euid x = 1, which are moving in the j/-direction with velocities 1, such as in Figure 6. 

Figure 6 Plane Couette flow with velocity 1 on the plates...

M. Renardy, A rigorous stability proof for plane Couette flow of an uppe-convected Maxwell fluid at zero Reynolds number, Eur. J. Mech. B, 11 (1992) 511-516. 

M. Renardy and Y. Renardy, Linear stability of plane Couette flow of an upper-convected Maxwell fluid, J. Non-Newtonian Fluid Mech., 22 (1986) 23-33. 

C.H. Li, Stability of two superposed elastoviscous liquids in plane Couette flow, Phys. Fluids, 12 (1969) 531-538. 

Problem 3-17. Plane Couette Flow Driven by Oscillating Shear Stress. Consider an initially motionless incompressible Newtonian fluid confined between two infinite plane boundaries separated by a gap width d as depicted in the figure. Suppose the plane y = 0 is oscillated back and forth with an oscillatory shear stress r = to sin cot. 

Problem 3-19. Start-Up of Plane Couette Flow Driven by a Constant Shear Stress. 

Problem 3-34. Temperature Distribution in Plane Couette Flow Due to a Linearly... 

Increasing Wall Temperature. In this problem you will examine convective heat transfer in plane Couette flow. Suppose we have the channel depicted in the figure ... 

Fluid inertia effects have been found to be very small for the cone-and-plate geometries typically supplied with these instruments. While inertial corrections are foimd to be imimportant for the parallel plate geometries, for shearing gaps of the order of 2 mm or less (except possibly for very thin fluids), they must be taken into accoimt in the concentric cylinder geometry (especially for high-density, mobile fluids). Evaluation methods are available for p, in the case of cylindrical and plane Couette flow, taking into account fluid inertia [Aschoff and Schummer, 1993]. 

Robertson, J.M., Johnson, H.F. (1970). Turbulence structure in plane Couette flow. Journal of... 

Sharipov F, Cumin LMG, Kalempa D (2004) Plane Couette flow of binary gaseous mixture in the whole range of the Knudsen number. Eur J Mech B/Fluids 23 899-906... 

Sone Y, Takata S, Ohwada T (1990) Numerical analysis of the plane Couette flow of a rarefied gas on the basis of the linearized Boltzmann equation for hard sphere molecules. Eur J Mech B/Fluid 9 273-288... 

Another example is plane Couette flow with variable viscosity [13,14]. Consider the steady flow of an incompressible Newtonian fluid between two infinite parallel plates separated by a distance, a, as shown in Eigure 6.2. Each plate is maintained at a temperature Tq. The upper plate is allowed to move... 

Next, we consider the special case of a plane Couette flow with the velocity given by v(r) = 7J/e, where e is a unit vector in ar-direction and 7 = dvx/dy = const is the shear rate. Furthermore, for simplicity, the motion of the particle is restricted to the xy-plane. Then the equations of motion correspond to the (two-dimensional version) of the SLLOD algorithm used in NEMD simulation studies of the viscous properites of fluids [10] ... 

FENE potentials. A treatment of a plane Poiseuille flow similar to the plane Couette flow considered here is feasible. The influence of confining... 

ROBERTSON, J M. "On turbulent plane Couette flow", 6th Mid West Conference on Fluid Mech., Univ. of Texas 1959. 

Fig. 12 Schematic diagram for planar approximations, (a) Axial generalized plane Couette flow (b) helical flow in a very thin annulus.

When the above transformations are used with the earlier expressions for axial generalized annular Couette flow and the limit as e-+0 is evaluated, the results for the axial generalized plane couette flow can be obtained. 

Verma, P.D., Bhatt, B.S., 1973. Plane Couette flow of two immiscible incompressible fluids with uniform suction at the stationary plate. Proc. Indian Acad. Sci. India A 78, 108-120. 

For the Poiseuille flow presented in the previous two sections, the flow was induced by a pressure difference applied between the two ends of a straight pipe. The plane Couette flow makes it possible to study the way how a force is applied to move a solid wall, without pushing the fluid in contact with the wall, and can generate a flow due to viscosity. The fluid is held between two parallel plates of infinite length (Figure 1.5). One of the plates, at z = 0, is kept stationary. The other... 

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