External Mass and Heat Transfer

So far we have approximated the external heat and mass transfer coefficients by virtue of an average value however, precise measurements have indicated that the local value may substantially change along the catalyst surface. Moreover, for a highly exothermic reaction a very strong gas phase concentration and temperature gradients may occur so that the pellet is bathed by a nonuniform external field (13, 14). 

Here we consider a spherical catalyst pellet with negligible intraparticle mass- and negligible heat-transfer resistances. Such a pellet is nonporous with a high thermal conductivity and with external mass and heat transfer resistances only between the surface of the pellet and the bulk fluid. Thus only the external heat- and mass-transfer resistances are considered in developing the pellet equations that calculate the effectiveness factor rj at every point along the length of the reactor. 

If the external heat and mass transfer resistances are negligible, eqs 7 and 8 can be simplified by replacing the unknown surface values ci)S and Ts with the known conditions in the bulk fluid phase, and then transform to the following simple boundary conditions at the external pellet surface ... 

This methods depends on the implicit assumption that the uptake rate is controlled entirely by intracrystalline diffusion in an isothermal system, with all other resistances to either mass or heat transfer negligible. This is a valid approximation if diffusion is sufficiently slow or if the zeolite crystals are sufficiently large but the dominance of intracrystalline diffusional resistance should not be assumed without experimental verification. In many practical systems, particularly with small commercial zeolite crystals, the external heat and mass transfer resistances are in fact dominant. A detailed discussion of such effects has been given by Lee and Ruthven(5-7). 

Accounting for the influences of external heat and mass transfer resistances in limiting the sorption rates, in many instances reasonable agreement between diffusion data from sorption experiments and PFG NMR may... 

The physical aspects involved are heat transfer and mass transfer. The external heat and mass transfers are free of resistance under the environment of fluidized beds. Only the interna heat and mass transfers are treated here. To develop the mathematic model, the following assumptions and statements are made ... 

FIG. 12-15 Drying curves and corresponding moisture gradients for situations involving external heat and mass-transfer control and internal mass-transfer control. 

Drying kinetics, which are affected by temperature, particle size, and structure, are limited by external heat and mass transfer to and from the particle surface in the early stages, but internal moisture transport is the main parameter at lower moisture. 

Vapor-phase, fixed-bed process performance usually stays the same or improves as the reactor length is increased because any influence of external heat and mass transfer would diminish upon scale-up. Diameter has no effect as long as the reactants are. 

Pang, S., External Heat and Mass Transfer Coefficients for Kiln Drying of Timber, Drying Technology, 1996, 14(3 4), pp. 859-871. 

More recently, a detailed study of diffusion of the xylene isomers in large crystals of NaX and natural faujasite was undertaken by both sorption rate and tracer exchange.(11-14) The data obtained by both these techniques using several different crystal sizes were entirely consistent but the diffusivities were much smaller than the values derived for the same systems by NMR PFG measurements. In an attempt to resolve this discrepancy we have developed a new chromatographic technique (zero length column or ZLC) which is less sensitive than conventional sorption methods to the intrusion of external heat and mass transfer resistances and which is therefore useful for following relatively rapid diffusion processes. The method has now been applied to study the diffusion of a range of different hydrocarbons in both A and X zeolite crystals and the results of these studies are summarized here. 

If the experimental results of Kehoe and Butt [114] in Figs. 3.7.a-2 and 3.7.a-3 are studied, note that the external heat transfer resistance can be appreciable, and, especially for the isothermal pellet, must be considered. The same mass and heat balance equations (3.7.a-l, 2) [or (3.7.a-8,9)] are used, but surface boundary conditions expressed in terms of the finite external heat and mass transfer resistances are used. 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (94) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to products in the presence of heat and mass transfer limitations. We shall find this term convenient for use throughout the remainder of the chapter. Global rate expressions then include both external heat and mass transfer effects on the reaction rate and the efficiency with which the internal... 

External heat and mass transfer effects are to be neglected in your analysis, but you should estimate the potential magnitudes of these effects. 

Effective thermal conductivity and effective moisture diffusivity are related to internal heat and mass transfer, respectively, while air boundary heat and mass transfer coefficients are related to external heat and mass transfer, respectively. The above transport properties are usually coefficients in the corresponding flow rate and driving force relationship. The equilibrium material moisture content, on the other hand, is usually related to the mass transfer driving force. 

The PB models are based on continuous description of coupled external heat and mass transfer from gas to droplet and PB approach for the intradroplet mass transfer phenomenon of solid component [11,12]. The PB approach has only been applied to the growth of suspended particles in droplet until the recent treatment of aggregation [10,13]. It is worth noting that the PB method is generally suitable for droplets containing suspended, not dissolved, solid components. 

In conventional drying, the controlled parameters are the dry- and wet-bulb temperatures as well as the velocity of the airflow. These three parameters determine the external heat- and mass-transfer rates ... 

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