Couette flow approximation

If the shear is equal to the wall shear throughout the region of interest, Eq. 6.170 reduces to the Couette flow approximation... 

Early theories for transpiration of air into air [114, 115] were based on the Couette flow approximation. Reference 114 extended the Reynolds analogy to include mass transfer by defining a two-part boundary layer consisting of a laminar sublayer and a fully turbulent core. Here, t = 0 in the sublayer (y < y ), and t = OAy and (i = 0 in the fully turbulent region. The density was permitted to vary with temperature. The effect of foreign gas injection in a low-speed boundary layer was studied in Ref. 116, and all these theories were improved upon in Ref. 117. 

In the Couette flow inside a cone-and-plate viscometer the circumferential velocity at any given radial position is approximately a linear function of the vertical coordinate. Therefore the shear rate corresponding to this component is almost constant. The heat generation term in Equation (5.25) is hence nearly constant. Furthermore, in uniform Couette regime the convection term is also zero and all of the heat transfer is due to conduction. For very large conductivity coefficients the heat conduction will be very fast and the temperature profile will... 

The attractive feature of LADM Is that once the fluid structure Is known (e.g., by solution of the YBG equations given In the previous section or by a computer simulation) then theoretical or empirical formulas for the transport coefficients of homogeneous fluids can be used to predict flow and transport In Inhomogeneous fluid. For diffusion and Couette flow In planar pores LADM turns out to be a surprisingly good approximation, as will be shown In a later section. 

According to this approximate condition, Couette flow will be stable for... 

If 22 = 0, for example, the Rayleigh criterion indicates that Couette flow is unstable for any 12]. On the other hand, the approximate stability criterion (12-158) for a viscous fluid says that the system will remain stable for... 

Long lasting simple shear flow of constant shear rate is often approximated by Couette flow. The liquid is between two concentric cylinders, one of which is rotating. If the ratio between the radii of the inner and outer cylinders is close to unity, W is nearly constant throughout the... 

The thermal boundary layer about a flying object may to a first order be approximated by a Couette flow. Let the velocity of the object be U and its surface emissivity be ew. The viscosity, thermal conductivity, and temperature of the ambient are fi k, and Too, respectively. Assume the ambient to be transparent and the curvature effects to be negligible. We wish to determine the steady surface temperature of the object. 

In both cases, the increase in rotation speed in the range of 1000-3000 rpm, which corresponds to arange of Ta from about 2000-6000 for the test device, resulted in a substantial increase in flux with a transition point observed at a rotation speed of 2000 rpm—this corresponds approximately to a Taylor number of 3500, where turbulent Couette flow can be assumed. 

It is feasible to relate the rate of drag reduction decrease to degradation kinetics as a function of shear stress. The above approximate relationships must be refined through use of more data on final degradation levels and degradation rates both in couette flow and in pipes using the same solutions in both. 

For the case of comparatively high concentrations and no Brownian movement, Gold and Guth calculated the following approximate formula for Couette flow and rigid rod-like particles (comp. Table 83). ... 

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

In the glass-steel contacts with pure sliding conditions, the temperature difference also varies at the dimple zone. The couette flow would equal to the entrainment speed at the inlet zone approximately because the temperature difference is very small. However, at the contact area, the flow decreases as is passing downstream because the... 

Reply bv the Authors We make the assumption that the parabolic temperature approximation is adequate in regions where reverse (Poisseuille dominated) flow takes place, even though it is strictly only true for planar Couette flow. To do anything better would also mean abandoning the mean cross-film viscosity assumption, which would make the modelling much more complex. The mean film temperature therefore bears the same relationship to the contact surface temperatures as elsewhere. Compression effects and increasing shear in the inlet region lead to a small rise... 

We now investigate the Couette flow of a nematic liquid crystal in precisely the same type of experiment discussed above for an anisotropic fluid described in Fig. 5.8 and in essence follow the work of Atkin and Leslie [6]. The one-constant approximation for the nematic elastic energy will be assumed in order to simplify the presentation ... 

Figure 2-9. A number of simple flow geometries, such as concentric cylinder (Couette), cone-and-plate, and parallel disk, are commonly employed as rheometers to subject a liquid to shear flows for measurement of the fluid viscosity (see, e.g., Fig. 3-5). In the present discussion, we approximately represent the flow in these devices as the flow between two plane boundaries as described in the text and sketched in this figure.

Hence, to achieve the best possible approximation to a linear shear flow, the Couette device must have a very thin gap relative to the cylinder radius. 

Measurement of the flow properties of non-Newtonian fluids is typically accomplished via rotational techniques. The rotational methods fall into two basic types concentric cylinder and cone and plate rheometers. In a concentric cylinder rheometer, a bob is placed inside a cylinder so that the fluid to be studied may be placed into the gap between the cyhnders. This arrangement helps approximate a uniform shear rate throughout a sample by shearing only a thin film of sample fluid between the cyhnders. In the Searle method, the inner cylinder is rotated so that interchangeable bobs can be used (to vary the gap). The outer cylinder does not rotate making it easier to apply a temperature control jacket. In the Couette method, the outer cylinder turns. In each case, the torque on the inner bob is measured. 

De Kepper has described a fascinating pattern of waves that can be studied in a continuous couette reactor. This is an open spatial reactor that provides a good approximation of a one-dimensional diffusion system, and consists of two concentric cylinders with a narrow gap between them. The inner cylinder can rotate while the outer one is fixed. At each end of the cylinder is a chamber fitted with a stirrer into which reactants can flow in and products flow out. Variation of the rate of rotation causes changes in the... 

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