Mass transfer analogous correlations

Heat Transfer Heat-transfer rates are gener ly large despite severe axial dispersion, with Ua. frequently observed in the range 18.6 to 74.5 and even to 130 kW/(m K) [1000 to 4000 and even to 7000 Btu/(h fF °F)][see Bauerle and Ahlert, Ind. Eng. Chem. Process Des. Dev., 4, 225 (1965) and Greskovich et al.. Am. Tn.st. Chem. Eng. J., 13,1160 (1967) Sideman, in Drewet al. (eds.). Advances in Chemical Engineering, vol. 6, Academic, New York, 1966, p. 207, reviewed earlier work]. In the absence of specific heat-transfer correlations, it is suggested that rates be estimated from mass-transfer correlations via the heat-mass-transfer analogy. 

The mass transfer correlations are obtained by replacing Nu by Sh and Pr by Sc according to the heat and mass transfer analogy. 

The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

Turbulent Flow. Perhaps the best known heat-transfer correlation for fully developed turbulent flow is that owing to Dittus and Boelter.27 The mass transfer analogy based on the Dittus-Boelter correlation is ... 

In order to use equation (8-15) for determination of T it is necessary to know the value of hGtkr known as the psychrometric ratio. Values of hG and ky can be estimated independently for the particular shape of the wetted surface by correlations like those presented in Chapter 2, using the heat- and mass-transfer analogy if necessary. Alternatively, experimental values of the psychrometric ratio can be used. Henry and Epstein (1970) have examined the data and methods of measurement and have produced some measurements of their own. For turbulent flow of gases past cylinders, such as wet-bulb thermometers, and past single spheres, the results of 18 gas-vapor systems are well correlated by... 

Jaturonglumlert and Kiatsiriroat (2010) considered heat and mass transfer for the combined convective and FIR drying of fruit leather, and found that the ratio between the heat and mass transfer coefficients for the combination technique could not be obtained from the heat-mass transfer analogy. Hence, modified correlations for predicting the ratio of heat and mass transfer coefficients in term of the heat transfer Nusselt number were developed. 

Mass-transfer coefficients must be those associated with die individual liquid and gas phases overall coefficients wilt not serve. The correlations of Chap. 6 wiU provide these for Berl saddles and Raschig rings, and additional data are summarized in Ref. 14. The Ic-type coefficients are not suitable because in some cases the transfer is opposite the concentration gradient, but k can be converted into F s (Table 3.1). Similarly data in the form of /// can be converted into Fa [Eqs. (8.24) and (8.3l)j. Heat-transfer coefficients can be estimated, if not otherwise available, through the heat- mass-transfer analogy. For the gas, the correction for mass transfer [Eq. (3.70)] provides... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Clulton-Colbum analogy (35). This semi-empirical relationship was developed for correlating mass- and heat-transfer data in pipes and is based on the turbulent boundary layer model... 

The convective mass transfer coefficient hm can be obtained from correlations similar to those of heat transfer, i.e. Equation (1.12). The Nusselt number has the counterpart Sherwood number, Sh = hml/Di, and the counterpart of the Prandtl number is the Schmidt number, Sc = p/pD. Since Pr k Sc k 0.7 for combustion gases, the Lewis number, Le = Pr/Sc = k/pDcp is approximately 1, and it can be shown that hm = hc/cp. This is a convenient way to compute the mass transfer coefficient from heat transfer results. It comes from the Reynolds analogy, which shows the equivalence of heat transfer with its corresponding mass transfer configuration for Le = 1. Fire involves both simultaneous heat and mass transfer, and therefore these relationships are important to have a complete understanding of the subject. 

In packed beds, mass transfer coefficients are often correlated by means of a Chilton—Colburn factor, Ju, analogous to their Jh heat transfer (Sect. 4.4.4)... 

As mentioned in Chapter 2, close analogies exist between the film coefficients of heat transfer and those of mass transfer. Indeed, the same type of dimensionless equations can often be used to correlate the film coefficients of heat and mass transfer. 

An analogy exists between the transfers of heat and mass in moving fluids, such that correlations of heat transfer involving the Prandtl number are valid for mass transfer when the Prandtl number Cp/k is replaced by the Schmidt number p pkd. This is of particular value in correlating heat transfer from small particles to fluids where particle temperatures are hard to measure but measurement of mass transfer may be feasible, for example, in vaporization of naphthalene. 

In order to aid in the design of dryers by analogy, examples of dimensions and performances of the most common types of dryers are cited in this chapter. Theory and correlation of heat and mass transfer are treated in detail elsewhere in this book, but their use in the description of drying behavior will be indicated here. 

Accuracy of an Analogy Between Heat and Mass Transfer and the Lewis Correlation for Conditioners and Cooling Towers... 

Experimental values of mass transfer coefficients can be collected as dimensionless correlations. One collection of these correlations is in Table II (Cussler, 1997). Because heat transfer is mathematically so similar to mass transfer, many assert that other correlations can be found by adapting results from the heat transfer literature. While this is sometimes tme, the analogy is frequently overstated because mass transfer coefficients normally apply across... 

More recent correlations for gas holdup and mass transfer include the effect of pressure and bimodal bubble size distribution (small and large bubbles), in a manner analogous to the treatment of dilute and dense phases in fluidized beds [see, e.g., Letzel et ah, Chem. Eng. Set, 54 (13) 2237 (1999)]. 

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