Mass transfer factor

Figures 4.34 and 4.35 represent two extreme cases. Drying processes represent the case shown in Fig. 4.34 and distillation processes represent Fig. 4.35. Neither case represents a convective mass transfer case while the gas flow is in the boundary layer, other flows are Stefan flow and turbulence. Thus Eqs. (4.243) and (4.244) can seldom be used in practice, but their forms are used in determining the mass transfer factor for different cases.

Considering the case of Eq. (4.244), it is normal to describe a real mass transfer case by taking into consideration the boundary layer flows and the turbulence by using a mass transfer factor which is defined by... 

Based on this, it is normal to define a mass transfer factor consistent with this case, analogous with Eq. (4.245) ... 

With the use of Eqs. (4.255) and (4.256a), the following relationships between the mass transfer factors are obtained ... 

In practice the mass transfer factors are often presented without stating the experimental assumptions by which = -/g or /g = 0 has been obtained. The designer has to decide on the suitability of the experiments from which the quantity or is measured. 

Strictly speaking, a new mass transfer factor should be defined that represents the situation Ma/a = 3. 

The preceding discussion has attempted to formulate the situation for laminar boundary layer flow as accurately as possible and to obtain precise correlation between the heat transfer and mass transfer factors. 

This allows the mass transfer factor to be calculated. The above equation can be refined to... 

To calculate the conductance of the boundary layer we first calculate rhf mass transfer factor using Eq. (4.300) ... 

The mass transfer factors with heterogeneous reactions the reaction rate may be controlled by the rates of diffusion of the reacting species rather than the chemical kinetics. 

Correlations for Mass Transfer Factors (jD) in Packed Beds... 

Fig. 5.30 Mass transfer factor as a function of Reynolds number for spherical fluid particles ...

Fig. 7.14 Area-free mass transfer factors, Sh/ Sc, for drops.

A reasonable upper limit on the mass transfer factor from bubbles to well-purified water at room temperature is given by ... 

Fig. 8.8 Mass transfer factor kAjA for dissolution of CO2 bubbles in aqueous solutions.

There are two useful measures of the effect of bounding walls on the heat- or mass-transfer rate. A mass transfer factor can be defined based on the same relative velocity between the particle and the fluid ... 

The surface velocities of Haberman and Sayre (HI), when used in the thin concentration boundary layer equation for circulating spheres, Eq. (3-51), yield the mass transfer factors and X d shown in Fig. 9.7 for k <2. For a fluid sphere in creeping flow the relationship between the mass transfer factors is... 

Sherwood number factor defined by Eq. (9-22) velocity ratio defined by Eq. (9-25) mass transfer factor defined by Eq. (9-21) thermal conductivity of continuous, dispersed phase velocity ratio defined by Eq. (9-7) viscosity ratio defined by Eq. (9-8)... 

However, at high velocities the effective value of the diffusivity of the solute dramatically increases as a result of induced radial flow, eventually reducing the resistance to mass transfer factor to virtually zero. This results in a corresponding dramatic reduction in the value of (H). Finally, at very high velocities, the greatly reduced longitudinal diffusion effect again dominates. At this point, the value of (H) is very small and, in fact, decreases even further as the mobile phase velocity is further increased. ... 

Various combination of shapes of isotherms and mass transfer factors have been taken into account by solutions of the problem in the literature. One of the simpler cases was adopted by Hougen and Marshall (1947, see Figure 15.13), who took a linear isotherm and diffusion to the external surface as controlling the rate. They developed the solution in analytical form, of which several approximations that are easier to use are mentioned for instance by Vermeulen et al. (1984, p. 16.28). A graphical form of the solution appears in Figure 15.13. This shows the effluent concentration ratio,... 

The mass transfer factor has also been correlated as a function of the Reynolds number only and thus taking account only of hydrodynamic conditions. If e is the voidage of the packed bed and the total volume occupied by all of the catalyst pellets is Vp, then the total reactor volume is Vp/(l - e). Hence the rate of mass transfer of component A per unit volume of reactor is NASx(l - e)/Vp. If we now consider a case in which only external mass transfer controls the overall reaction rate we have ... 

The absorption column design represents a compromise between mass transfer factors and economic considerations. The final design specification is for a column of 1.8 m diameter, approximately 32 m high, and containing 59 sieve trays. 

Another measurement is that of the concentration of dissolved oxygen. This additional measurement can provide useful information about the mass-transfer factor k a and the concentration of dissolved CO2 once combined with the algorithm presented earlier. 

This is shown schematically in Fig. 41. The downwardly directed curve on the left-hand side of Fig. 41 for the fixed bed implies that increased flow is by no means sufficient to raise the heat or mass-transfer factor proportionately to the increased pressure drop. Similarly, for single particles, neither a larger particle diameter nor a higher flow rate could compensate for the relatively limited increase in the transfer factor. 

AG Free energy change AGt Free energy of activation ff Critical humidity Ji Chilton-Colburn mass transfer factor... 

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