Boundary-layer development

Fig. 4. Boundary layer development around a circular cylinder where A represents the point of separation.

Boundary-layer development. The boundary layer that develops within an impeller passage causes the flowing fluid to experience a smaller exit area as shown in Figure 6-23. This smaller exit is due to small flow (if any) within the boundary layer. For the fluid to exit this smaller area, its velocity must increase. This increase gives a higher relative exit velocity. 

The rate of polymerization, as well as the mobility of macromolecules at the contact zone, is affected by the presence of the filler near the matrix. This results in a reduction of the number of possible conformations of molecules in the boundary layer developed, causing the formation of a denser material in the boundary layer than in the bulk. 

Moreover, in many cases, a shift of Tg to lower values of temperature has been detected, but in these cases the quality of adhesion between phases may be the main reason for the reversing of this attitude 11,14). If calorimetric measurements are executed in the neighbourhood of the glass transition zone, it is easy to show that jumps of energies appear in this neighbourhood. These jumps are very sensitive to the amount of filler added to the matrix polymer and they were used for the evaluation of the boundary layers developed around fillers. 

Hull, L. M., and W. M. Rohsenow, 1982, Thermal Boundary Layer Development in Dispersed Flow Film Boiling, MIT Heat Transfer Lab. Rep. 85694-104, Massachusetts Institute of Technology, Cambridge, MA. (4)... 

Figure 4 Hydrodynamic boundary layer development on the semi-infinite plate of Prandtl. <5D = laminar boundary layer, <5t = turbulent boundary layer, /vs = viscous turbulent sub-layer, <5ds = diffusive sub-layer (no eddies are present solute diffusion and mass transfer are controlled by molecular diffusion—the thickness is about 1/10 of <5vs)> B = point of laminar—turbulent transition. Source From Ref. 10.

Fig. 14. Thermal boundary-layer development. Freon-22, T, = 60°C. After Henry and Fouske (1975).

We also need to develop the theories for hquid film coefficient to use in the aforementioned equations. For drops that are close to spherical, without separation, Levich (1962) assumed that the concentration boundary layer developed as the bubble interface moved from the top to the bottom of a spherical bubble. Then, it is possible to use the concepts applied in Section 8.C and some relations for the streamlines around a bubble to determine Kl. ... 

Consider a long cylindrical shell whose interior is filled with an incompressible fluid. If the fluid is initially at rest when the cylinder begins to rotate, a boundary layer develops as the momentum diffuses inward toward the center of the cylinder. The fluid s circumferential velocity vu comes to the cylinder-wall velocity immediately, owing to the no-slip condition. At very early time, however, the interior fluid will be only weakly affected by the rotation, with the influence increasing as the boundary layer diffuses inward. If the shell continues to rotate at a constant angular velocity, the fluid inside will eventually come to rotate as a solid body. 

For relatively minor species, such as the CO mass fractions shown in Fig. 17.20, there are somewhat larger differences between the Navier-Stokes and boundary-layer models. Under these flow conditions the CO mass-fraction peaks just near the leading edge of the active catalyst. As the CO desorbs from the initial region of the catalyst, the shapes of the CO contours show less classical boundary-layer development behavior, especially at low Reynolds number. Nevertheless, the agreement between the two models is still quite good. 

An extended version of the hybrid technique of PIV/LIF/SIT is reported by Kitagawa et al. (2005), in which the PTV technique is employed to measure the velocity field in liquid phase and track the velocity distribution of dispersed bubbles, in addition to the SIT measurement of bubbles shape and location in a microbubble-laden turbulent channel flow. It is well known that microbubbles injected into the turbulent boundary layer developing on a solid wall have a significant skin friction reduction effect. To investigate the interactions between the injected microbubbles (the void fraction is actually low but... 

In contrast, Dunlap and Rushton [34] succeeded to correlate their measurements at cooling and heating in a vessel with a turbine stirrer and pipe bundle heat exchangers with Vis-0 4 because a thick boundary layer developed around the tubes. 

Consider fully developed flow in a pipe. A thermal boundary condition is applied, starting at a distance x = x<,. For the four different cases listed below, sketch the temperature profiles in the pipe as the thermal boundary layer develops, and the temperature profiles after the thermal boundary layer has fully developed ... 

Galbraith, R.A. and Head, M.R., Eddy Viscosity and Mixing Length from Measured Boundary Layer Developments , Aeronautical Quarterly, Vol. 26, pp. 133-154,1975. 

Initially, the boundary-layer development is laminar, but at some critical distance from the leading edge, depending on the flow field and fluid properties, small disturbances in the flow begin to become amplified, and a transition process takes place until the flow becomes turbulent. The turbulent-flow region may be pictured as a random churning action with chunks of fluid moving to and fro in all directions. The transition from laminar to turbulent flow occurs when... 

Consider the flow in a tube as shown in Fig. 5-3. A boundary layer develops at the entrance, as shown. Eventually the boundary layer fills the entire tube, and the flow is said to be fully developed. If the flow is laminar, a parabolic velocity profile is experienced, as shown in Fig. 5-3a. When the flow is turbulent, a somewhat blunter profile is observed, as in Fig. 5-3b. In a tube, the Reynolds number is again used as a criterion for laminar and turbulent flow. 

The plate under consideration need not be heated over its entire length. The situation which we shall analyze is shown in Fig. 5-9, where the hydrodynamic boundary layer develops from the leading edge of the plate, while heating does not begin until x = x0. 

While the engineer may frequently be interested in the heat-transfer characteristics of flow systems inside tubes or over flat plates, equal importance must be placed on the heat transfer which may be achieved by a cylinder in cross flow, as shown in Fig. 6-7. As would be expected, the boundary-layer development on the cylinder determines the heat-transfer characteristics. As long as the boundary layer remains laminar and well behaved, it is possible to compute the heat transfer by a method similar to the boundary-layer analysis of Chap. 5. It is necessary, however, to include the pressure gradient in the analysis because this influences the boundary-layer velocity profile to an appreciable extent. In fact, it is this pressure gradient which causes a separated-flow region to develop on the back side of the cylinder when the free-stream velocity is sufficiently large. 

Consider the vertical flat plate shown in Fig. 7-1. When the plate is heated, a free-convection boundary layer is formed, as shown. The velocity profile in this boundary layer is quite unlike the velocity profile in a forced-convection boundary layer. At the wall the velocity is zero because of the no-slip condition it increases to some maximum value and then decreases to zero at the edge of the boundary layer since the free-stream conditions are at rest in the free-convection system. The initial boundary-layer development is laminar but at... 

For laminar airflow in a tube, when 8 approaches the tube radius, Poiseuille flow or a parabolic flow profile is fully developed. This is accomplished by the acceleration of the central portion of the flow. However, when Re exceeds a value lying somewhere between 104 and 106, the laminar boundary layer becomes so thick that it is no longer stable, and a turbulent boundary layer develops. 

Results of an analysis has been presented here for spatial stability properties of a mixed convection boundary layer developing over a heated horizontal fiat plate. A similarity solution (as given by (6.3.11) and (6.3.13)) for the mean flow is used following Schneider (1979). Such boundary layers are characterized by the buoyancy parameter K = Gr and is solved... 

A laminar boundary layer develops on the upwind side of a cylinder (Fig. 7-8). This layer is analogous to the laminar sublayer for flat plates (Fig. 7-6), and air movements in it can be described analytically. On the downwind side of the cylinder, the airflow becomes turbulent, can be opposite in direction to the wind, and in general is quite difficult to analyze. Nevertheless, an effective boundary layer thickness can be estimated for the whole cylinder (to avoid end effects, the cylinder is assumed to be infinitely long). For turbulence intensities appropriate to field conditions, in mm can be represented as follows for a cylinder ... 

We have seen that a velocity boundary layer develops when a fluid flows over a surface as a result of the fluid layer adjacent to the surface assuming the surface velocity (i.e., zero velocity relative to the surface). Also, we defined the velocity boundary layer as the region in which the fluid velocity varies from zero to 0.99V. Likewise, a thermal boundary layer develops when a fluid at a specified temperature flows over a surface that is at a different temperature, as shown in Fig. 6-15. 

The convection heat transfer rate anywhere along (he surface is directly related to the temperature gradient at that location. Therefore, the shape of the temperature profile in the thermal boundary layer dictates the convection heat transfer between a solid surface and the fluid flowing over it. In flow over a heated (or cooled) surface, both velocity and thermal boundary layers develop... 

C Wilt a thermal boundary layer develop in flow over a surface even if both the fluid and the surface arc at the same temperature ... 

Liquid metals such as mercury have high thermal conductivities, and are commonly used in applications that require high heat transfer rates. However, they have very small Prandtl numbers, and thus the thermal boundary layer develops much faster than the velocity boundary layer. Then we can assume the velocity in the thermal boundary layer to be constant at the free stream value and solve the energy equation. It gives... 

Th regioii of flow over which the thermal boundary layer develops and re.iches (he tube center i.s called the thermal entrance region, and the length of this region is called the thermal entry length L,. Flow in the thermal... 

Although piston motion may be rapid, a perfect adiabatic compression does not occur in an RCM. Heat losses to the chamber wall and boundary layer development as a result of the gas motion generated by the piston are the main causes of departures from ideality. Nevertheless, gas at the core of the compressed charge may be regarded to have experienced an adiabatic isentropic compression, assuming heat losses are confined to the boundary layer. 

If the thermally conductive body is bounded by a fluid, a boundary layer develops in the fluid. The heat flux into the fluid, with a as the heat transfer coefficient is... 

If a quiescent body (1) is bounded by a moving fluid (2) a diffusion boundary layer develops in the fluid. Instead of (2.348), the boundary condition... 

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