Local transfer rates

Figure 5 shows conduction heat transfer as a function of the projected radius of a 6-mm diameter sphere. Assuming an accommodation coefficient of 0.8, h 0) = 3370 W/(m -K) the average coefficient for the entire sphere is 72 W/(m -K). This variation in heat transfer over the spherical surface causes extreme non-uniformities in local vaporization rates and if contact time is too long, wet spherical surface near the contact point dries. The temperature profile penetrates the sphere and it becomes a continuum to which Fourier s law of nonsteady-state conduction appfies. 

I. Turbulent, local flat plate, natural convection, vertical plate Turbulent, average, flat plate, natural convection, vertical plate Nsk. = — = 0.0299Wg=Ws = D x(l + 0.494W ) )- = 0.0249Wg=W2f X (1 + 0.494WE )- [S] Low solute concentration and low transfer rates. Use arithmetic concentration difference. Ncr > 10 " Assumes laminar boundary layer is small fraction of total. D [151] p. 225... 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Economizer corrosion rates are enhanced by higher heat-transfer rates excessive heat flux may create localized nucleate boiling zones where gouging, as a result of chemical concentration effects, can occur. Air heaters are also located in the exit gas system. They do a job similar to that of economizers except that they preheat combustion air. 

Most theoretical studies of heat or mass transfer in dispersions have been limited to studies of a single spherical bubble moving steadily under the influence of gravity in a clean system. It is clear, however, that swarms of suspended bubbles, usually entrained by turbulent eddies, have local relative velocities with respect to the continuous phase different from that derived for the case of a steady rise of a single bubble. This is mainly due to the fact that in an ensemble of bubbles the distributions of velocities, temperatures, and concentrations in the vicinity of one bubble are influenced by its neighbors. It is therefore logical to assume that in the case of dispersions the relative velocities and transfer rates depend on quantities characterizing an ensemble of bubbles. For the case of uniformly distributed bubbles, the dispersed-phase volume fraction O, particle-size distribution, and residence-time distribution are such quantities. 

Characteristic length [Eq. (121)] L Impeller diameter also characteristic distance from the interface where the concentration remains constant at cL Li Impeller blade length N Impeller rotational speed also number of bubbles [Eq, (246)]. N Ratio of absorption rate in presence of chemical reaction to rate of physical absorption when tank contains no dissolved gas Na Instantaneous mass-transfer rate per unit bubble-surface area Na Local rate of mass-transfer per unit bubble-surface area Na..Average mass-transfer rate per unit bubble-surface area Nb Number of bubbles in the vessel at any instant at constant operating conditions N Number of bubbles per unit volume of dispersion [Eq. (24)] Nb Defined in Eq. (134)... 

Bonamy L., Thuet J. M., Bonamy J., Robert D. Local scaling analysis of state-to-state rotational energy-transfer rates in N2 from direct measurements, J. Chem. Phys. 95, 3361-70 (1991). 

The local mass transfer rate is related to the concentration gradient by... 

Eqs. (40H41) are obtained from the analytical solution using the first two terms in the 0-series expansion of the concentration profile. As a result, they are accurate only for small values of meridional angle, 8. To correct for large values of 6, Newman [45] used Lighthill s transformation and Eq. (15) for the meridional velocity gradient to calculate the local mass transfer rate as Sc - oo. His numerical result is plotted in Fig. 5 in the form of Shloc/Re1/2 Sc1/3 vs. 8 as the thin solid line. The dashed line is... 

Fig. 5. Local mass transfer rate on the surface of a rotating hemisphere in laminar flow. Here the meridional angle, 9, is given in degrees.

For turbulent flow, we shall use the Chilton-Colburn analogy [12] to derive an expression for mass transfer to the spherical surface. This analogy is based on an investigation of heat and mass transfer to a flat plate situated in a uniform flow stream. At high Schmidt numbers, the local mass transfer rate is related to the local wall shear stress by... 

The Chilton-Colburn analogy can be also used to estimate the local mass transfer rate in laminar flow where the wall shear stress is related to the azimuthal velocity gradient by... 

Of considerable interest is the use of small isolated electrodes, in the form of strips or disks embedded in the wall, to measure local mass-transfer rates or rate fluctuations. Mass-transfer to spot electrodes on a rotating disk is represented by Eqs. (lOg-i) of Table VII. Analytical solutions in this case have to take account of curved streamlines. Despic et al. (Dlld) have proposed twin spot electrodes as a tool for kinetic studies, similar to the ring-disk electrode applications of disk and ring-disk electrodes for kinetic studies are discussed in several monographs (A3b, P4b). In fully developed channel or pipe flow, mass transfer to such electrodes is given by the following equation based on the Leveque model ... 

Overall mass-transfer rates at a sphere in forced flow, and mass-transfer rate distribution over a sphere as a function of the polar angle have been measured by Gibert, Angelino, and co-workers (G2, G4a) for a wide range of Reynolds numbers. The overall rate dependence on Re exhibited two distinct regimes with a sharp transition at Re = 1250. Local mass-transfer rates were deduced from measurements in which the sphere was progressively coated by an insulator, starting from the rear. 

Weder s experiments were carried out with opposing body forces, and large current oscillations were found as long as the negative thermal densification was smaller than the diffusional densification. [Note that the Grashof numbers in Eq. (41) are based on absolute magnitudes of the density differences.] Local mass-transfer rates oscillated by 50%, and total currents by 4%. When the thermal densification dominated, the stagnation point moved to the other side of the cylinder, while the boundary layer, which separates in purely diffusional free convection, remained attached. 

Rao et al. (R7) first made local mass-transfer measurements, by ring electrodes embedded in the perforated plates between which a packed bed was contained. They measured the local mass-transfer rate at ring electrodes... 

Another case of multimedia fate modeling may be exemplified by human inhalation exposure estimates for PCB spills. The spill size is estimated considering both spread and soil infiltration. Volatilization calculations were carried out to get transfer rates into the air compartment. Finally, plume calculations using local meteorological statistics produced ambient concentration patterns which can be subsequently folded together with population distributions to obtain exposures. 

Chemical separation of technetium in soils is not easy, but it is fairly well-known that under aerobic conditions pertechnetate Tc(YII) is readily transferred to plants while under anaerobic conditions insoluble TcCh (or its hydrate) is not transferred to them. Even under aerobic conditions, however, the transfer rate decreases with time [28], indicating that soluble pertechnetate changes to insoluble forms by the action of microorganisms which produce a local anaerobic condition around themselves [29,30]. Insoluble technetium species may be TcOz, sulfide or complexes of organic material such as humic acid. 

When the electron coupling between locally excited-state (LE) and charge transfer state (CT) is weak, the electron transfer rate kcl can be expressed as (7)... 

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