Sherwood number shape

Sherwood number shape and Hamiltonian consistent standard hydrogen electrode stereochemical descriptor (as in the si face)... 

The transfer coefficient can be correlated in the form of a dimensionless Sherwood number Sh(= h0dp/D). The particle diameter dp is often taken to be the diameter of the sphere having the same area as the (irregular shaped) pellet. Thaller and Thodos(38> correlated the mass transfer coefficient in terms of the gas velocity u and the Schmidt number Sc(= p/pD) ... 

Sherwood number (Ksasdp/atD) shape factor interstitial velocity... 

Schmidt number n/pD Sherwood number Ksdh/D surface area of packing particle packing-shape factor residence time interstitial velocity superficial velocity empty column volume volume of packing particle Weber number a/pdl... 

In (1.196) the quantities c,n,m still depend on the type of flow, laminar or turbulent, and the shape of the surface or the channel over or through which the fluid flows. Correspondingly, the mean Sherwood number can be written as... 

Periodic cellular structures of the type used for almost all automotive catalyst supports are described by a few simple parameters (2, 3). If the cell density, wall thickness, and channel shape are known, the surface area, open area, channel hydraulic diameter, friction factor, Nusselt Numbers, and Sherwood Number are all obtained. And from these expressions the various properties of interest for... 

Tables 4.2 shows the values of II for particles of various shape (according to [94, 166]). It follows from (4.3.5) that the mean Sherwood number can be obtained from the data in this table by dividing the shape factor by the surface area of the particle and then multiplying by the characteristic length.

Sherwood number. For solid particles, drops, and bubbles of spherical shape, the mean Sherwood number can be calculated according to the formula... 

Peclet numbers, the problem of mass exchange between a particle of arbitrary shape and a uniform translational flow were studied by the method of matched asymptotic expansions in [62]. The following expression was obtained for the mean Sherwood number up to first-order infinitesimals with respect to Pe ... 

The following general statement was proved in [63] for the case of a uniform translational Stokes flow (Re -4 0) or a potential flow past a particle of an arbitrary shape the mean Sherwood number remains the same if the flow direction is changed to the opposite. 

For a steady-state viscous flow (without closed streamlines) past arbitrarily shaped smooth particles, one can calculate the mean Sherwood number by the approximate formula [359]... 

For a translational Stokes flow past a convex body of revolution of sufficiently smooth shape with symmetry axis parallel to the flow, the error (in percent) in formula (4.10.9) for the mean Sherwood number can be approximately estimated as follows ... 

Here Sho is the Sherwood number corresponding to mass transfer of a particle in a stagnant medium without the reaction. Each summand in (5.3.6) must be reduced to a dimensionless form on the basis of the same characteristic length. The value of Sho can be determined by the formula Sho = all/S , where a is the value chosen as the length scale and, is the surface area of the particle the shape factor II is shown in Table 4.2 for some nonspherical particles. 

Low Peclet numbers. In [347] it was proved that for an arbitrary dependence of the diffusion coefficient on concentration and for any shape of particles and drops, the following asymptotic formula is valid for the mean Sherwood number at low Peclet numbers ... 

The limiting Sherwood number of 2.0 corresponds to an effective film thickness of DJ2 if the mass-transfer area is taken as the external area of the sphere. The concentration gradients actually extend out to infinity in this case, but the mass-transfer area also increases with distance from the surface, so the effective film thickness is much less than might be estimated from the shape of the concentration profile. 

Consider a flow-through electrolyser with plate-shaped electrodes in a rectangular channel (Fig. 3). In this case, the Sherwood number is given as... 

The limiting Sherwood number is probably between 6 and 10 the value will depend on the bed porosity and particle shape. 

Table 28.2. Asymptotic values of Nusselt/Sherwood numbers and friction factors for different monolith channel shapes. Adapted from Ref. 11.

In the film model, Nusselt and Sherwood numbers need to be determined. The analogy between heat and mass transfer suggests that Nu Sh. Extensive work has been devoted to the variation of these numbers with distance, and to their asymptotic values in very long channels of various shapes (Shah and London (1978)). Heck et al. (1976) showed that upstream the light-off point, the asymptotic wall heat flux Nusselt number must be used, whereas the asymptotic wall... 

To calculate the mean Sherwood (Nusselt) number in the case of a free-poured layer of particles of various shape, one can use the following empiric formulas [254] in a wide range of Reynolds numbers ... 

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