Boundary layers general discussion

The details of the transitions and the vortex behavior depend on the actual channel dimensions and wall-temperature distributions. In general, however, for an application like a horizontal-channel chemical-vapor-deposition reactor, the system is designed to avoid these complex flows. Thus the ideal boundary-layer analysis discussed here is applicable. Nevertheless, one must exercise caution to be sure that the underlying assumptions of one s model are valid. 

The resulting residence times, which are shown in Fig. 7-28 by the dashed line, should still be considered upper limits in view of the fact that values for K2 in the planetary boundary layer generally are smaller than 20 m2/s. Junge (1957) and Fabian and Junge (1970) have shown how one can, in principle, incorporate the variation of Kz in the boundary layer. This refinement will not be discussed, however, because meteorological conditions in the boundary layer are too variable for a generalized model to be applicable. 

In the previous section we discussed wall functions, which are used to reduce the number of cells. However, we must be aware that this is an approximation that, if the flow near the boundary is important, can be rather crude. In many internal flows—where all boundaries are either walls, symmetry planes, inlets, or outlets—the boundary layer may not be that important, as the flow field is often pressure determined. However, when we are predicting heat transfer, it is generally not a good idea to use wall functions, because the convective heat transfer at the walls may be inaccurately predicted. The reason is that convective heat transfer is extremely sensitive to the near-wall flow and temperature field. 

Depending on the context, we sometimes prefer the term interphase over interface because the latter refers to an infinitely sharp dividing plane between two phases. Organisms generally form boundary layers, e.g. the cell wall, that are characterised by a gradual transition from the biological phase to the medium phase, and if we discuss the volume properties of such layers the term interphase is more appropriate. 

The discussion so far has concentrated on mass transfer. The transfer of the heat liberated on adsorption or consumed on desorption may also limit the rate process or the adsorbent capacity. Again the possible effects of the boundary-film and the intra-pellet thermal properties have to be considered. A Biot number for heat transfer is hri/ke. In general, this is less than that for mass transfer because the boundary layer offers a greater resistance to heat transfer than it does to mass transfer, whilst the converse is true in the interior of the pellet. 

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. 

Water can reduce adhesion strength by reducing the strength of the metal oxide layer via hydration52,81 . Hydration of the oxide layer is detrimental because the resulting aluminum-, iron-, or other metal-hydrates generally exhibit very poor adhesion to their base metals 52 Therefore, the produced layer of hydrates will effectively act as a weak boundary layer in the system and decrease adhesion strength. Since the hydration reaction has been most heavily studied on aluminum oxides, the authors have chosen to base the discussion of the hydration mechanism on this case. 

The effect of concentration polarization on specific membrane processes is discussed in the individual application chapters. However, a brief comparison of the magnitude of concentration polarization is given in Table 4.1 for processes involving liquid feed solutions. The key simplifying assumption is that the boundary layer thickness is 20 p.m for all processes. This boundary layer thickness is typical of values calculated for separation of solutions with spiral-wound modules in reverse osmosis, pervaporation, and ultrafiltration. Tubular, plate-and-ffame, and bore-side feed hollow fiber modules, because of their better flow velocities, generally have lower calculated boundary layer thicknesses. Hollow fiber modules with shell-side feed generally have larger calculated boundary layer thicknesses because of their poor fluid flow patterns. 

Solutions to the boundary layer equations are, today, generally obtained numerically [6],[7],[8],[9],[10],[11],[12]. In order to illustrate how this can be done, a discussion of how the simple numerical solution procedure for solving laminar boundary layer problems that was outlined in Chapter 5 can be modified to apply to turbulent boundary layer flows. For turbulent boundary layer flows, the equations given earlier in the present chapter can, because the fluid properties are assumed constant, be written as ... 

Eckert, E.R.G. and Soehnghen. E., "Interferometric Studies on the Stability and Transition to Turbulence of a Free-Convection Boundary Layer , Proc. of the General Discussion on Heat Transfer, pp. 321-323. ASME-1ME. London. 1951. 

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