Gas phase convection

The lean/gas phase convection contribution has received the least attention in the literature. Many models in fact assume it to be negligible in comparison to dense phase convection and set hl to be zero. Compared to experimental data, such an approach appears to be approximately valid for fast fluidized beds where average solid concentration is above 8% by volume. Measurements obtained by Ebert, Glicksman and Lints (1993) indicate that the lean phase convection can contribute up to 20% of total... 

Table 12.1 gives a summary of the dimensionless variables. Two additional groups have been added, the Weber number, We, to account for droplet formation and the Nusselt number, Nu = hj/k, to account for gas phase convection. A corresponding Nusselt... 

Although the mixing patterns in bubble columns do not obviously correspond to simple axial dispersion, the dispersed plug flow model has been found to hold reasonably well in practice. For a two-phase gas-liquid system, the equation for gas-phase convection and dispersion (Chapter 2, equation 2.14) becomes ... 

The gas phase convection terms and gravity forces are negligible. 

It has been shown that liquid moisture transfer still exists in the sorption region and is a strong funetion of free water content. Scientists studied gas phase convective transport in the dry region, which contains irreduc-... 

There will also be heat loss from tire substrate due to convection cuiTents caused by the teirrperamre differential in the suiTounding gas phase, but this will usually be less than the radiation loss, because of the low value of the heat transfer coefficient, / , of gases. The heat loss by this mechanism, Qc, can be calculated, approximately, by using tire Richardson-Coulson equation... 

When a gas reacts with a solid, heat will be transfened from the solid to the gas when the reaction is exothermic, and from gas to solid during an endothermic reaction. The energy which is generated will be distributed between the gas and solid phases according to the temperature difference between the two phases, and their respective thermal conductivities. If the surface temperature of the solid is T2 at any given instant, and that of the bulk of the gas phase is Ti, the rate of convective heat transfer from the solid to the gas may be represented by the equation... 

Pollard and Newman" have also studied CVD near an infinite rotating disk, and the equations we solve are essentially the ones stated in their paper. Since predicting details of the chemical kinetic behavior is a main objective here, the system now includes a species conservation equation for each species that occurs in the gas phase. These equations account for convective and diffusive transport of species as well as their production and consumption by chemical reaction. The equations stated below are given in dimensional form since there is little generalization that can be achieved once large chemical reaction mechanisms are incorporated. 

The gas-phase mass flux of species k at the surface is a combination of diffusive and convective processes. 

Figure 10. Streamlines (top) and relative gas phase composition of A1 species (bottom) In a vertical axlsymmetrlc reactor at five different times during growth of an AlAs/GaAs superlattice. Red corresponds to all A1 species, violet to no A1 species. The corner Insert portrays the variation In solid fraction of A1 across the Interface. Forced convection dominated flow.

Evaporated film catalysts are virtually always used with a static gas phase, and with reactant gas pressures less than about 100 Torr. One thus relies upon gaseous diffusion and convection for transport to the catalyst surface. However, provided one is dealing with reaction times of the order of minutes to tens of minutes, gas phase transport has but a negligible effect on the reaction, provided none of the reaction volume is separated from the film by small bore tubulation. Beeck et al. (77) in fact originally used an all-glass magnetically coupled turbine for gas circulation, but this is only... 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

An alternate to the concept of cluster renewal discussed above is the concept of two-phase convection. This second approach disregards the separate behavior of lean and dense phases, instead models the time average heat transfer process as if it were convective from a pseudo-homogeneous particle-gas medium. Thus h hcl, hh and hd are not... 

Many investigators consider neutralization as a poorly understood process in the gas phase. While in the best possible cases it may be considered as a homogeneous second-order process, detailed experimentation in specific cases sometimes fails to establish that (Freeman, 1968 Meisels, 1968). At low dose rates and low gas pressures, wall effects can be seen as a major inhibiting factor, as most neutralizations would then be expected to occur on the walls. Coating the wall with specific chemicals has not lead to a uniform conclusion. On the other hand, wall effects are also present at high dose rates. In such cases, and with gas pressure greater than about 0.1 atm, normal positive ions cannot reach the walls if the size of the vessel is 10 cm or more (Freeman, 1968). Even for electrons, it is hard. Large-scale convection is supposed to be the chief transport mechanism this, however, is difficult to establish experimentally. 

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