Boundary layer portion

Normally the vortex finder should extend down into the conical portion of the cyclone. It is thought that the vortex finder plays an important role in the maintenance of a stable spiraling fluid flow in the cyclone, and this makes it more difficult for the particles to leak through the boundary layer on the roof of the lid of the cyclone to the overflow tube.- Without a vortex finder, the efficiency may be reduced by 4-5%. However, an excessive long vortex finder may hinder the high spin velocity in the fluid flow and thus reduce the efficiency of the cyclone. 

It is precisely the loosening of a portion of polymer to which the authors of [47] attribute the observed decrease of viscosity when small quantities of filler are added. In their opinion, the filler particles added to the polymer melt tend to form a double shell (the inner one characterized by high density and a looser outer one) around themselves. The viscosity diminishes until so much filler is added that the entire polymer gets involved in the boundary layer. On further increase of filler content, the boundary layers on the new particles will be formed on account of the already loosened regions of the polymeric matrix. Finally, the layers on all particles become dense and the viscosity rises sharply after that the particle with adsorbed polymer will exhibit the usual hydrodynamic drag. 

It should be noted that for polymerization-modified perlite the strength parameters of the composition algo go up with the increasing initial particle size. [164]. In some studies it has been shown that the filler modification effect on the mechanical properties of composites is maximum when only a portion of the filler surface is given the polymerophilic properties (cf., e.g. [166-168]). The reason lies in the specifics of the boundary layer formation in the polymer-filler systems and formation of a secondary filler network . In principle, the patchy polymerophilic behavior of the filler in relation to the matrix should also have place in the failing polymerization-modified perlite. 

The flow of fluid over a plane surface, heated at distances greater than. to from the leading edge, is now considered. As shown in Figure 11.11 the velocity boundary layer starts at the leading edge and the thermal boundary layer at a distance o from it. If the temperature of the heated portion of the plate remains constant, this may be taken as the datum temperature. It is assumed that the temperature at a distance y from the surface may be represented by a polynomial of the form ... 

It may be assumed that the fully turbulent portion of the boundary layer starts at y+ — 30, that the ratio of the mixing length to the distance y from the surface, Af/v = 0.4, and that for a smooth surface u+ = I4 at v 30. 

The control volume in the gas phase (Figure 9.19) is considered as stationary, steady and responds fast to any changes transmitted from the condensed phase. A portion of the water used in suppression is evaporated in the flame. The flame is a thickness of <5R within the boundary layer. Kinetic effects are important in this region where essentially all of the combustion occurs. The conservation relationships follow ... 

In terms of hydrodynamics, the boundary layer thickness is measured from the solid surface (in the direction perpendicular to a particle s surface, for instance) to an arbitrarily chosen point, e.g., where the velocity is 90-99% of the stream velocity or the bulk flow ((590 or (599, respectively). Thus, the breadth of the boundary layer depends ad definitionem on the selection of the reference point and includes the laminar boundary layer as well as possibly a portion of a turbulent boundary layer. 

As Re increases further and vortices are shed, the local rate of mass transfer aft of separation should oscillate. Although no measurements have been made for spheres, mass transfer oscillations at the shedding frequency have been observed for cylinders (B9, D6, SI2). At higher Re the forward portion of the sphere approaches boundary layer flow while aft of separation the flow is complex as discussed above. Figure 5.17 shows experimental values of the local Nusselt number Nuj c for heat transfer to air at high Re. The vertical lines on each curve indicate the values of the separation angle. It is clear that the transfer rate at the rear of the sphere increases more rapidly than that at the front and that even at very high Re the minimum Nuj. occurs aft of separation. Also shown in Fig. 5.17 is the thin concentration boundary layer... 

Table 5.4, so that these equations are recommended for general use. The -power term in Eq. (F) can be viewed as the contribution from the portion of the sphere with a laminar boundary layer forward of separation, while the 0.71-power term corresponds to the section aft of separation. Justification for the latter power is found from local Sh values as discussed in the next chapter. 

For Re < 110 the wake is closed and laminar as discussed above. Transfer over the front portion of the cap is again described by Eq. (8-20). Transfer from the base occurs by diffusion into the wake fluid as it moves along the bubble base, producing a concentration boundary layer. The solute in this... 

In Example 8.5, we saw how the diffusive boundary layer could grow. The boundary never achieves 1 m in thickness or even 5 cm in thickness, because of the interaction of turbulence and the boundary layer thickness. The diffusive boundary layer is continually trying to grow, just as the boundary layer of Example 8.5. However, turbulent eddies periodically sweep down and mix a portion of the diffusive boundary layer with the remainder of the fluid. It is this unsteady character of the turbulence... 

Figure 6.22 illustrates the solution to this problem for several Reynolds numbers. The boundary layer forms near the inlet boundary, owing to the axial no-slip condition. The inner portions of the flow (i.e., near the centerline) tend to behave as an inviscid fluid, as evidenced by the linear v profile. As expected, the boundary layer thins as the Reynolds number increases. 

An alternative to the standard-form representation is the differential-algebraic equation (DAE) representation, which is stated in a general form as g(r, y, y). The lower portion of Fig. 7.3 illustrates how the heat equation is cast into the DAE form. The boundary conditions can now appear as algebraic constraints (i.e., they have no time derivatives). For a problems as simple as the heat equations, this residual representation of the boundary conditions is not necessary. However, recall that implicit boundary-condition specification is an important aspect of solving boundary-layer equations. 

Absorption of olefin from olefin/paraffin mixtures has been scaled up to the pilot plant scale, and a number of successful trials were performed in the early 1990s. Separation factors of 200 or more were obtained, producing 99.7 % pure ethylene. However, slow degradation of the silver nitrate solution is a problem, and a portion of the recirculating degraded silver nitrate solution must be bled off and replaced with fresh solution continuously. Boundary layer problems on the liquid side of the membrane are also a serious issue in these devices [21]. 

Consideration is given to the streamline portion of the boundary layer in Section 11.3 where, assuming ... 

The high vertical flux of particulates in river/estuarine plume regions commonly results in the accumulation of particles in the formation of a benthic boundary layer (BBL) and/or mobile and fluid muds (see chapter 6 for more details). The BBL is defined by Boudreau and Iprgensen (2001, p. 1) as those portions of sediment and water columns that are affected directly in the distribution of their properties and processes by the presence of... 

Benthic boundary layer those portions of sediment and water columns that are affected directly in the distribution of their properties and processes by the presence of the sediment-water interface. 

The mean velocity distribution in the outer portion of the turbulent boundary layer on a flat plate is approximately given by ... 

---