Bulk/mass

In order to evaluate Eq. (5-23) in the neighborhood of the boiling crisis for given local bulk conditions (i.e., fluid pressure, bulk mass flow rate, quality, and equivalent diameter), the following simplifications are made. 

Because the components of the analytical expression for C are not sufficiently known to permit an analytical evaluation, C is determined empirically as a function of the local quality at the point of DNB, XDNB, (under nonuniform heat flux conditions) and the bulk mass flux, G. The empirically determined expression for C is... 

Such effects are especially observable when polymerisation occurs in the bulk (mass polymerisation). In this case, another effect can be observed at high... 

It is difficult to obtain how the diffusivity depends on concentration using the bulk mass loss or gain method, although it is possible to verify specific concentration dependence by conducting experiments from small degrees of mass loss to almost complete mass loss (Wang et al., 1996). On the other hand, the shape of diffusion profiles reveals the dependence of diffusivity on concentration. 

This surface evolution equation has the same form as the bulk mass diffusion equation the concentration is replaced by the height of the surface, h, and the diffusivity is replaced by Bv. 

Aside from the original assumption of a lumped analysis, thus far there have been no other assumptions or approximations to the model. The model relies completely on basic thermodynamic principles, a known cell performance R(I), and rigorous mathematical operations. To solve the model, we need to know the bulk mass and heat capacity of the cell, M and C, respectively the reactant supply flow rate (m = fuel flow + air flow) the inlet temperature and pressure and the change in stream composition due to the electrochemical reaction, AX, so that the change in enthalpy can be calculated the electrical load current, / and the inlet and exit temperatures, Tm and rout. 

We consider a mixture of n reacting constituents which are endowed with a microstructure and assume that every place x in the body is simultaneously occupied by a material particle of each constituent which is present at time r. Each constituent has its own bulk mass density (>,. 

The flux Na is the sum of the diffusive flux JA with respect to the center of mass plus the contribution to the flux of A caused by the bulk mass movement. 

Mass transfer can result from several different phenomena. There is a mass transfer associated with convection in that mass is transported from one place to another in the flow system. This type of mass transfer occurs on a macroscopic level and is usually treated in the subject of fluid mechanics. When a mixture of gases or liquids is contained such that there exists a concentration gradient of one or more of the constituents across the system, there will be a mass transfer on a microscopic level as the result of diffusion from regions of high concentration to regions of low concentration. In this chapter we are primarily concerned with some of the simple relations which may be used to calculate mass diffusion and their relation to heat transfer. Nevertheless, one must remember that the general subject of mass transfer encompasses both mass diffusion on a molecular scale and the bulk mass transport, which may result from a convection process. 

As the water evaporates, it will diffuse upward through the air, and at steady state this upward movement must be balanced by a downward diffusion of air so that the concentration at any x position will remain constant. But at the surface of the water there can be no net mass movement of air downward. Consequently there must be a bulk mass movement upward with a velocity just large enough to balance the diffusion of air downward. This bulk mass movement then produces an additional mass flux of water vapor upward. 

Steps 2 and 6 are both pore diffusion processes with apparent activation energies between 2 and 10 kcal/mol. This apparent activation energy is stated to be about 1/2 that of the chemical rate activation energy. The concentration of reactants decreases from the outer perimeter towards the center of the catalyst particle for Step 2. In this case some of the interior of the catalyst is being utilized but not fully. Therefore the effectiveness factor is greater than zero but considerably less than one. These reactions are moderately influenced by temperature but to a greater extent than bulk mass transfer. 

Because of the significant differences in temperature dependence the kinetically limited reactions can be distinguished from pore diffusion that in turn can be differentiated from bulk mass transfer. This is shown in Fig. 7.2 in... 

Fig. 7.2. Conversion of a reactant vs. temperature.The concentration of reactants [R] within the porous catalyst structure. Concentration of R is (a) uniform for kinetic control, (b) decreasing within the catalyst for pore diffusion control, and (c) zero immediately at the surface of the catalyst for bulk mass transfer.

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