Sherwood numbers local

Using Eqs. (36)-(39), one obtains the following expressions for the local Sherwood number and local limiting current density on the speherical surface... 

Figure 3.11 shows the local Sherwood number, Shj, for the limits of high and low Pe. Values for Pe — 0.1 are not symmetrical about the equator, and show the greatest transfer rates over the leading surface indicating that the... 

Fig. 3.11 Local Sherwood number for rigid sphere in Stokes flow (1) Exact numerical solution Pe = 10 (2) High Pe asymptotic solution (L3) Pe = 10 (3) Low Pe asymptotic solution (A2) Pe = 0.1.

For flow parallel to a cylinder the rate of mass or heat transfer decreases with axial distance. Far from the leading end, the transfer at low Pe may be considered as transfer from a line source into a uniform stream and the local Sherwood number becomes... 

Fig. 5.16 Local Sherwood number for a sphere with Sc = 0.71. Numerical results of Woo (W9).

Fig. 5.19 Local Sherwood number for a sphere Solid lines are the numerical results of Woo (W9) and Hatim (Hll) at the values of Re and Sc indicated. Points are the data of Frossling (F3) for sublimation of naphthalene into air.

The mechanism of mass transfer to the external flow is essentially the same as for spheres in Chapter 5. Figure 6.8 shows numerically computed streamlines and concentration contours with Sc = 0.7 for axisymmetric flow past an oblate spheroid (E = 0.2) and a prolate spheroid (E = 5) at Re = 100. Local Sherwood numbers are shown for these conditions in Figs. 6.9 and 6.10. Figure 6.9 shows that the minimum transfer rate occurs aft of separation as for a sphere. Transfer rates are highest at the edge of the oblate ellipsoid and at the front stagnation point of the prolate ellipsoid. 

Fig. 6.9 Local Sherwood number for an oblate and Epstein (M6). Axial flow.

Introducing the local mass transfer coefficient kx and the local Sherwood number by the expressions... 

Rose [47,48] applies the analogy by replacing the local Nusselt number in Eq. 14.44 with the local Sherwood number ... 

The resulting expression relates the local Sherwood number to the local Reynolds number, the Schmidt number, and the parameter p. A second equation relating these quantities results from the condition that the interface is impermeable to the noncondensable gas... 

However, in the specific case of honeycomb catalysts with square channels, which is most frequent in SCR applications, the latter dependence is practically negligible, and an excellent estimate of the local Sherwood number, Sh, is provided by the Nusselt number from solution of the Graetz-Nusselt (thermal) problem with constant wall temperature, Nut, which is available in the heat transfer literature (113). The following correlation was proposed, accounting also for development of the laminar velocity profile ... 

As long as the conversion is below the value of the right-hand side term, the external diffusion limitations can be neglected. On the other hand, the external mass transfer can be taken into account by a mass transfer coefficient for which Beretta et al. [45] derived the following correlation based on a functional form for the local Sherwood number to interpolate the exact solution ... 

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