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No-slip

On no-slip walls zero velocity components can be readily imposed as the required boundary conditions (v = v, = 0 on F3 in the domain shown in Figure 3.3). Details of the imposition of slip-wall boundary conditions are explained later in Section 4.2. [Pg.96]

Imposition of no-slip velocity conditions at solid walls is based on the assumption that the shear stress at these surfaces always remains below a critical value to allow a complete welting of the wall by the fluid. This iraplie.s that the fluid is constantly sticking to the wall and is moving with a velocity exactly equal to the wall velocity. It is well known that in polymer flow processes the shear stress at the domain walls frequently surpasses the critical threshold and fluid slippage at the solid surfaces occurs. Wall-slip phenomenon is described by Navier s slip condition, which is a relationship between the tangential component of the momentum flux at the wall and the local slip velocity (Sillrman and Scriven, 1980). In a two-dimensional domain this relationship is expressed as... [Pg.98]

Figure 5.14 (a) The predicted velocity field corresponding to no-slip wall boundary conditions, (b) Tlie predicted velocity field corresponding to partial slip boundary conditions... [Pg.159]

Figure 5.15 (a) The predicted temperature distribution eorresponding to the no-slip... [Pg.160]

After the imposition of no-slip wall boundary conditions the last term in Equation (5.64) vanishes. Therefore... [Pg.179]

The force is direcdly proportional to the area of the plate the shear stress is T = F/A. Within the fluid, a linear velocity profile u = Uy/H is estabhshed due to the no-slip condition, the fluid bounding the lower plate has zero velocity and the fluid bounding the upper plate moves at the plate velocity U. The velocity gradient y = du/dy is called the shear rate for this flow. Shear rates are usually reported in units of reciprocal seconds. The flow in Fig. 6-1 is a simple shear flow. [Pg.630]

This problem requires use of the microscopic balance equations because the velocity is to he determined as a function of position. The boundary conditions for this flow result from the no-slip condition. AU three velocity components must he zero at the plate surfaces, y = H/2 and y = —H/2. [Pg.635]

Boundary layer flows are a special class of flows in which the flow far from the surface of an object is inviscid, and the effects of viscosity are manifest only in a thin region near the surface where steep velocity gradients occur to satisfy the no-slip condition at the solid surface. The thin layer where the velocity decreases from the inviscid, potential flow velocity to zero (relative velocity) at the sohd surface is called the boundary layer The thickness of the boundary layer is indefinite because the velocity asymptotically approaches the free-stream velocity at the outer edge. The boundaiy layer thickness is conventionally t en to be the distance for which the velocity equals 0.99 times the free-stream velocity. The boundary layer may be either laminar or turbulent. Particularly in the former case, the equations of motion may be simphfied by scaling arguments. Schhchting Boundary Layer Theory, 8th ed., McGraw-HiU, New York, 1987) is the most comprehensive source for information on boundary layer flows. [Pg.666]

Rare earth permanent magnets with no slip and not subject to decoupling. [Pg.62]

Supposing constant rotational speeds, no slip, and an axial inlet, the velocity triangles are as shown in Figure 6-10. For the radial vane, the absolute tangential fluid velocity at the impeller exit is constant—even if the flow rate is increased or decreased. [Pg.228]

Figure 8.3. VeJocily flow profile in a tube for a fluid with zero yield stress and assuming no slip at... Figure 8.3. VeJocily flow profile in a tube for a fluid with zero yield stress and assuming no slip at...
The first two eases represent the smallest and largest vent sizes required for a given rate at inereased pressure. Between these eases, there is a two-phase mixture of vapor and liquid. It is assumed that the mixture is homogeneous, that is, that no slip oeeurs between the vapor and liquid. Furthermore, the ratio of vapor to liquid determines whether the venting is eloser to the all vapor or all liquid ease. As most relief situations involve a liquid fraetion of over 80%, the idea of homogeneous venting is eloser to all liquid than all vapor. Table 12-3 shows the vent area for different flow regimes. [Pg.963]

The company concerned normally used slip-plates to isolate equipment under repair. On this occasion, no slip-plate was fitted because it was only a steam line. However, steam and other service lines in plant areas are easily contaminated by process materials, especially when there is a direct connection to process equipment. In these cases, the equipment under repair should be positively isolated by slip-plating or disconnection before maintenance. [Pg.6]

To obtain physically meaningful solutions, a set of appropriate boundary conditions must also be specified. One obvious requirement is that no fluid should pass through the boundary (i.e. wall) itself. Thus, if we choose a reference frame in which the boundaries are at rest, we require that v fi = 0, where fi is the unit normal to the surface. Another condition, the so-called no-slip condition ([trittSS], [feyn64]), is the requirement that the fluid s tangential velocity vanishes at the surface v x n = 0. [Pg.468]

If it is assumed that there is no slip between the liquid and the basket, a> is constant and a forced vortex is created. [Pg.53]

That the particles and liquid in the bed were travelling at the same velocity, i.e. there was no slip within the bed. [Pg.207]

In fluid dynamics it is generally assumed that the velocity of flow at a solid boundary, such as a pipe wall, is zero. This is referred to as the no-slip condition. If the fluid wets the surface, this assumption can be justified in physical terms since the molecules are... [Pg.670]

If the fluid does not wet the wall, the no-slip condition no longer applies and the pressure gradient at a given flowrate will be lower. This effect is particularly important with the flow of molten polymers, although it does not seem to be significant in other applications. [Pg.671]

Considink, D. M. 272 Consistency coefficient of fluids 108 Constitutive equations 111 Contact angle and no-slip condition 670 -----boiling 483... [Pg.872]

Wu and Cheng (2003) measured the friction factor of laminar flow of de-ionized water in smooth silicon micro-channels of trapezoidal cross-section with hydraulic diameters in the range of 25.9 to 291.0 pm. The experimental data were found to be in agreement within 11% with an existing theoretical solution for an incompressible, fully developed, laminar flow in trapezoidal channels under the no-slip boundary condition. It is confirmed that Navier-Stokes equations are still valid for the laminar flow of de-ionized water in smooth micro-channels having hydraulic diameter as small as 25.9 pm. For smooth channels with larger hydraulic diameters of 103.4-103.4-291.0pm, transition from laminar to turbulent flow occurred at Re = 1,500-2,000. [Pg.109]

The question of the conditions to be satisfied by a moving fluid in contact with a solid body was one of considerable difficulty for quite some time, as pointed out by Goldstein (1965), and the assumption of no-slip is now generally accepted for practical purposes. On the other hand, if we can make an artificial solid surface where there is very little interaction between the surface and the liquid in contact with it, slip would be appreciable for liquid flow. The analysis of the phenomenon was presented by Watanabe et al. (1999). [Pg.135]

If the range of the channel height is limited to be above 10 pm, then the no-slip boundary condition can be adopted. Furthermore, with the assumptions of uniform inlet velocity, pressure, density, and specified pressure Pout at the outlet, the boundary conditions can be expressed as follows ... [Pg.181]

The boundary conditions are as follows In Figure 3.2.2, z-axis component and r-axis component velocities are zero for (1) and (2), respectively. The gradients of other variables are zero for both the boundaries. The gradients of all variables are zero for (3) and (4). No slip condition and heat transfer from the flame kernel to the spark electrode are assumed for (5) and (6), at the surface of spark electrode. [Pg.27]

Finally the knowledge of the velocity profiles allows the determination of the actual shear rate exerted upon the liquid slab. For the bulk system some slip Is observed at the reservoir walls. No slip Is observed for the micropore fluid as a result of the high density close to the reservoir walls, which facilitates the momentum transfer between the reservoir and the liquid slab particles. [Pg.279]

At the solid walls, the boundary conditions state that the velocity is zero (i.e. no slip). Also at the walls, the temperature is either fixed or a zero-gradient condition is applied. At the surface of the spinning disk the gas moves with the disk velocity and it has the disk temperature, which is constant. The inlet fiow is considered a plug fiow of fixed temperature, and the outlet is modeled by a zero gradient condition on all dependent variables, except pressure, which is determined from the solution. [Pg.338]

No slip Is used as the velocity boundary conditions at all walls. Actually there Is a finite normal velocity at the deposition surface, but It Is Insignificant In the case of dilute reactants. The Inlet flow Is assumed to be Polseullle flow while zero stresses are specified at the reactor exit. The boundary conditions for the temperature play a central role in CVD reactor behavior. Here we employ Idealized boundary conditions In the absence of detailed heat transfer modelling of an actual reactor. Two wall conditions will be considered (1) adiabatic side walls, l.e. dT/dn = 0, and (11) fixed side wall temperatures corresponding to cooled reactor walls. For the reactive species, no net normal flux Is specified on nonreacting surfaces. At substrate surface, the flux of the Tth species equals the rate of reaction of 1 In n surface reactions, l.e. [Pg.357]


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