Boundary layer thickness cylinder

Boundary layer thickness variation around cylinder. 

This section describes selected mass transport correlations for laboratory devices such as the rotating disk and cylinder. These mass transport correlations may be used in order to establish the same mass transport conditions (diffusional boundary layer thicknesses) as those obtained in a pipe or under impinging flow. Essentially, the experimenter may vary the rotation rate and geometry of the cylinder or disk to dial in the same mass transport conditions as obtained in the field for pipes or impinging jets. The user should also verify that the same hydrodynamic conditions also exist through use of Reynolds numbers, as shown above. 

For vertical surfaces, the Nusselt and Grashof numbers are formed with L, the height of the surface as the characteristic dimension. If the boundary-layer thickness is not large compared with the diameter of the cylinder, the heat transfer may be calculated with the same relations used for vertical plates. The general criterion is that a vertical cylinder may be treated as a vertical flat plate [13] when... 

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 ... 

All of the flux equations used so far in this book have been for onedimensional cases. Because we have introduced the average thickness of the boundary layer for cylinders (Eq. 7.11) and spheres (Eq. 7.12), let us also consider the appropriate fluxes for such cases, which can have many biological applications. For cylindrical symmetry, can change in the radial direction perpendicularly away from the cylinder axis but not change with angle around the cylinder or with position along its axis. The heat flux... 

C. Assuming that the spines can be represented by cylinders that are 1.2 mm in diameter, what is their boundary layer thickness ... 

E.J. Lyford-Pike and J.B. Heywood, Thermal Boundary Layer Thickness in the Cylinder of a Spark Ignition Engine, Int. J. Heat Mass Trans. 27 (1984) 1873. 

Simplify the radial conduction term, (l/r)(9/9r)(r3r/3r), at large Prandtl numbers when the thermal boundary layer thickness is small relative to the radius of the cylinder. This is the locally flat approximation. 

Table 16-2 illustrates the functional dependence of ]criticai on the intrapellet Damkohler number, A. Notice that the numerical results for ]criticai = /(A) are identical for spheres and cylinders when A > 15. For all catalyst shapes, licriticai 1 in the diffusion-limited regime when A oo, and the mass transfer boundary layer thickness measured inward from the external surface of the catalyst becomes infinitesimally small. If equation (16-25), which defines / critical, is solved for A instead of ]criticab then ... 

Natural convection to blunt bodies such as cylinders (2-dimensional) and spheres (3-dimensional) has been studied by Acrivos (9) and from his analysis one can show that these configurations are characterized by constant boundary-layer thicknesses. For 2-dimensional bodies,... 

Figure 1 shows the geometry. Strictly speaking, equation 2 applies only to single cylinders in slow cross flow, for point particles with negligible deposition and with the thickness of boundary layer much less than the radius of the cylinder. 

It was shown above that the limiting c.d. increases with velocity raised to the 0.8 power and the pipe diameter raised to the -0.2 power for piping corrosion rates that are controlled by mass transport. In contrast, it is evident that the shear stress increases with the fluid velocity raised to the 1.75 power and the pipe diameter raised to the -0.2 power. Thus equality of shear stress does not give equality of mass transfer rates. In both cases corrosion is enhanced in pipes of smaller diameter for the same solution velocity. Such a relationship can be rationalized based on the effect of pipe diameter on the thickness of the mass transport and hydrodynamic boundary layers for a given fixed geometry. Cameron and Chiu (19) have derived similar expressions for defining the rotating cylinder rotation rate required to match the shear stress in a pipe for the case of velocity-... 

Figure 7-7. Mean thickness of the air boundary layer (a) adjacent to a flat leaf at various wind speeds indicated next to the curves and (b) adjacent to objects of three different shapes at a wind speed of 1 m s-1. The length for a flat leaf represents the mean distance across it in the direction of the wind the diameter is used for the bluff bodies represented by cylinders and sp heres. Values were determined using Equations 7.10 through 7.12. Note that 1.0 m s-1 equals 3.6 km hour-1 or 2.2 mile hour-1.

Nobel, PS. 1974. Boundary layers of air adjacent to cylinders. Estimation of effective thickness and measurements on plant material. Plant Physiol. 54 177-181. 

The boundary layer over a hot horizontal cylinder starts to develop at the bottom, increasing in thickness along the circumference, and forming a rising plume at the top, as shown in Fig. 9-12. Therefore, the local Nusselt number... 

In addition, a concentration boundary layer develops over the surface of the cylinder with its thinnest portion near the forward stagnation point. When the thickness of the concentration boundary layer is much less than the radius of the cylinder, the equation of convective diffusion simplifies to the familiar form for rectangular coordinates (Schlichling, 1979, Chapter XII) ... 

For the heated vertical plate and horizontal cylinder, the flow results from natural convection. The stagnation configuration is a forced flow. In each case the flow is of the boimdai7 Kiyer type. Simple analytical solutions can be obtained when the thickness of the du.st-free space is much smaller than that of the boundary layer. In this case the gas velocity distribution can be approximated by the first term in an expansion in the distance norroal to the surface. Expressions for the thickness of the dust-free space for a heated vertical surface and a plane stagnation flow are derived below. 

The thin-layer approximation fails because natural convective boundary layers are not thin. From the interferometric fringes in Fig. 4.2ft (which are essentially isotherms), the thermal boundary layer around a circular cylinder is seen to be nearly 30 percent of the cylinder diameter. For such thick boundary layers, curvature effects are important. Despite this failure, thin-layer solutions provide an important foundation for the development of correlation equations, as explained in the section on heat transfer correlation method. 

For a potential flow around the cylinder, the approximate solution of equations (19.26) gives S - = 0.0625. However, at Re 1, a viscous boundary layer of thickness <5 r /V is formed near the cylinder surface, which causes a stronger curving of streamlines near the surface than we would expect for a potential flow. As a result, trajectories are pushed away from the surface. This means that the number of droplets reaching the surface in a unit time decreases. We can ac-... 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Find the steady-state concentration profile during the radial diffusion of a diffusant through a bilayer cylindrical shell of inner radius, Rm, where each layer has thickness AR/2 and the constant diffusivities in the inner and outer layers are Dm and Dout. The boundary conditions are c(r = Rln) = cin and c(r = Rm + Ai ) = cout. Will the total diffusion current through the cylinder be the same if the materials that make up the inner and outer shells are exchanged Assume that the concentration of the diffusant is the same in the inner and outer layers at the bilayer interface. 

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