Mass-Transfer Coefficients for Various Geometries

The experimental data for mass-transfer coefficients obtained using various kinds of fluids, different velocities, and different geometries are correlated using dimensionless numbers similar to those of heat and momentum transfer. Methods of dimensional analysis are discussed in Sections 3.11, 4.14, and 7.8. 

The most important dimensionless number is the Reynolds number which indicates degree of turbulence. 

Other substitutions from Table 7.2-1 can be made fork in Eq.(7.3-3). The Stanton number occurs often and is 

Often the mass-transfer coefficient is correlated as a dimensionless factor which is related to k and as follows. 

3B Analogies Among Mass, Heat, and Momentum Transfer 

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Mass-Transfer Coefficient for Various Geometries. It is desired to estimate the... 

Correlations for the mass-transfer coefficient, as the Sherwood number for various membrane geometries have been reviewed (39). 

Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds various correlations exist in terms of dimensionless numbers. In Table 1 the most appropriate ones for laboratory reactors are given [5, 7, 30, 31]. Values of k( and h for gases in laboratory systems range between O.l-lOms-1 and 100-1000JK-1s-1 m-2, respectively. In the case of monoliths, other correlations should be used because of the different geometry [32-34],... 

Silverman has defined a number of useful expressions that allow one to utilize the rotating cylinder method with a variety of practical geometries (12,15). Both shear stresses and mass transfer coefficients are included in the derivations described (12). Table 1 in NACE standard TM-0270-72 summarized the various features of experimental systems for studying flow induced corrosion (22). 

The extraction of toluene and 1,2 dichlorobenzene from shallow packed beds of porous particles was studied both experimentally and theoretically at various operating conditions. Mathematical extraction models, based on the shrinking core concept, were developed for three different particle geometries. These models contain three adjustable parameters an effective diffusivity, a volumetric fluid-to-particle mass transfer coefficient, and an equilibrium solubility or partition coefficient. K as well as Kq were first determined from initial extraction rates. Then, by fitting experimental extraction data, values of the effective diffusivity were obtained. Model predictions compare well with experimental data and the respective value of the tortuosity factor around 2.5 is in excellent agreement with related literature data. 

There is an extensive literalure on solutions to (3.1) for various geometries and flow regimes. Many results are given by Levich (1962). Results for heat transfer, such as those discussed by Schlichting (1979) for boundary layer flows, are applicable to mass transfer or diffusion if the diffusion coefficient, D, is substituted for the coeflidenl of thermal diffusivity, K/pCp, where k is the thermal conductivity, p is the gas density, and Cp is the heat capacity of the gas. The results are directly applicable to aerosols for point panicles, that is, iip = 0. 

Both heat and mass transfer coefficients are influenced by thermal and flow properties of the air and, of course, by the geometry of the system. Empirical equations for various geometries have been proposed in the literature. Table 4.9 summarizes the most popular equations used for drying. 

Mass Transfer Coefficients in Ducts of Various Geometries for Laminar Flow... 

Euler—Lagrange models for bubbly flows are also known as DBMs and can be used to investigate various features ofbubble column reactors. In this section, we will give two examples of studies that were made with the aid of a DBM. In the first example, we will highhght how the geometry affects the flow features inside the bubble column, which can be characterized by axial dispersion coefficients. In the second example, we will highlight the interplay between flow, mass transfer, and chemical reaction inside a bubble column. 

Methods for solving mass and heat transfer problems. The convective diffusion equation (3.1.1) is a second-order linear partial differential equation with variable coefficients (in the general case, the fluid velocity depends on the coordinates and time). Exact closed-form solutions of the corresponding problems can be found only in exceptional cases with simple geometry [79,197, 270, 370, 516]. This is especially true of the nonlinear equation (3.1.17). Exact solutions are important for adequate understanding of the physical background of various phenomena and processes. They can serve as test solutions to verify whether the problem is well-posed or to estimate the accuracy of the corresponding numerical, asymptotic, and approximate methods. 

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