Mass transfer Chilton-Colburn analogy

On occasion one will find that heat-transfer-rate data are available for a system in which mass-transfer-rate data are not readily available. The Chilton-Colburn analogy provides a procedure for developing estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental or Jh data obtained with gases to predict hquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer, according to Eq. (5-308). 

For systems other than air-water vapor, the value of h /k c, may differ appreciably from unity, and the wet-bulb and adiabatic-saturation temperatures are no longer equal. For these systems the psychrometric ratio may be obtained by determining h /k from heat- and mass-transfer an ogies such as the Chilton-Colburn analogy [Ind. Eng. Chem., 26, 1183 (1934)]. For low humidities this analogy gives... 

For turbulent flow, we shall use the Chilton-Colburn analogy [12] to derive an expression for mass transfer to the spherical surface. This analogy is based on an investigation of heat and mass transfer to a flat plate situated in a uniform flow stream. At high Schmidt numbers, the local mass transfer rate is related to the local wall shear stress by... 

The Chilton-Colburn analogy can be also used to estimate the local mass transfer rate in laminar flow where the wall shear stress is related to the azimuthal velocity gradient by... 

In some kinds of equipment, data only on mass transfer rates may be known. From these, on the basis of the Chilton-Colburn analogy, corresponding values of heat transfer rates can be estimated. 

This method takes advantage of the rough proportionality between heat and mass transfer coefficients according to the Chilton-Colburn analogy, and employs only heat transfer coefficients for the process of condensation from a mixture. The sensible heat of the vapor is transferred through the gas film... 

The heat transfer coefficient can be calculated from the mass transfer coefficient by means of the Chilton-Colburn analogy, also called the factor analogy. The factors are defined as ... 

Another concept sometimes used as a basis for comparison and correlation of mass transfer data in columns is the Chilton-Colburn 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... 

FIGURE 14-47 When the friction or heat transfer coefficient is known, the mass transfer coefficient can be determiued directly from the Chilton-Colburn analogy. 

Assumptions 1 The low mass flux conditions exist so that the Chilton-Colburn analogy between heat and mass transfer is applicable (v/ill be verified). 2 Both air and naphthalene vapor are ideal gases. 

SOLUTION Spray paint cans are temperature tested by submerging them in an uncovered hot water bath. The rates of heat loss from the top surface of the bath by radiation, natural convection, and evaporation are to be determined. Assumptions 1 The low mass flux conditions exist so that the Chilton-Colburn analogy between heat and mass transfer Is applicable since the mass fraction of vapor in the air is low (about 2 percent for saturated air at 300 K). 2 Both air and water vapor at specified conditions are ideal gases (the error involved in this assumption is less than 1 percent). 3 Water is maintained at a uniform temperature of 50°C. 

A widely used expression for estimating mass transfer coefficients is the Chilton-Colburn analogy... 

In Figure 10.8 we have plotted the variation of the ratios of mass transfer coefficients 12/ 11 k i/k22 for an acetone-benzene-helium system considered in Example 11.5.3. The Chilton-Colburn analogy predicts that these ratios would be independent of Re, as shown by the horizontal lines in Figure 10.8. The von Karman turbulent model, on the other hand, predicts that the influence of coupling should decrease with increase in Re. The latter trend is in accord with our physical intuition. Depending on the driving forces for mass transfer, the Chilton-Colburn and the von Karman turbulent models could predict different directions of transfer of acetone (see, e.g., Krishna, 1982). 

Figure 10.8. Ratio /C12A115 which are elements of the zero-flux matrix of mass transfer coefficients [/c], as a function of the gas-phase Reynolds number. Mass transfer between a gaseous mixture of acetone (l)-benzene (2)-helium (3) and a liquid film containing acetone and benzene. Calculations by Krishna (1982) based on the von Karman turbulent film model and the Chilton-Colburn analogy.

Mass transfer coefficients for the gas-vapor phase may be estimated using the Chilton-Colburn analogy Eqs. 11.4.35 and 8.8.7... 

The next step is to compute the binary mass transfer coefficients. For this example we must make use of the Chilton-Colburn analogy as discussed above. The Schmidt numbers for the 1-2 binary pair is computed first... 

A comparison of the interactive film models that use the Chilton-Colburn analogy to obtain the heat and mass transfer coefficients with the turbulent eddy diffusivity models. 

Repeat Exercise 10.2 using the multicomponent generalization of the Chilton-Colburn analogy to estimate the mass transfer coefficients. 

Revise the analysis of Example 11.5.3 and show how a method based on the film models of Chapter 8 could be used to compute the rates of mass transfer. Then use the Krishna-Standart method (of Sections 8.3 and 8.8.3) and compute the molar fluxes. Binary pair mass transfer coefficients may be estimated using the Chilton-Colburn analogy. 

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