Film Coefficients of Heat and Mass Transfer

In the above equations, pi, Ejy, and v are eddy thermal diffusivity, eddy diffusivity, and eddy kinematic viscosity, respectively, all having the same dimensions (L- ). It should be noted that these are not properties of fluid or system, because 

values of h for heating or cooling increase with thermal conductivity k. Also, h values can be increased by decreasing the effective thickness of the laminar film 

Ay by increasing fluid velocity along the interface. Various correlations for predicting film coefficients of heat transfer are provided in Chapter 5. 

The film (individual) coefficients of mass transfer can be defined similarly to the film coefficient of heat transfer. A few different driving potentials are used today to define the film coefficients of mass transfer. Some investigators use the mole fraction or molar ratio, but often the concentration difference AC (kg or kmol m ) is used to define the liquid phase coefficient (m while the partial pressure difference A/i (atm) is used to define the gas film coefficient (kmolh m 2 atm ). However, using and A gp of different dimensions is not very convenient. In this book, except for Chapter 15, we shall use the gas phase coefficient (m h ) and the liquid phase coefficient ki (m h ), both of which are based on the molar concentration difference AC (kmol m ). With such practice, the mass transfer coefficients for both phases have the same simple dimension (L T ). Conversion between k and is easy, as can be seen from Example 2.4. 

By applying the effective film thickness concept, we obtain Equation 2.18 for the individual phase mass transfer coefficient k Q (LT ) which is analogous to Equation 2.17 for heat transfer. 

If the temperature gradient across the laminar sublayer and the value of thermal conductivity were known, it would be possible to calculate the rate of heat transfer by Equation 2.1. This is usually impossible, however, because the thickness of the 

Air is heated from 20 to 80 °C with use of an air heater. From operating data, the air-side film coefficient of heat transfer was determined as 44.2 kcal h 1 rn 2 C1. Estimate the effective thickness of the air film. The heat conductivity of air at 50 °C is 0.0481 kcal h 1 m-1 °C-1. 

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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. 

Because of the very small fluid channels (Re is very small), the flows in microreactor systems are always laminar. Thus, mass and heat transfers occur solely by molecular diffusion and conduction, respectively. However, due to the very small transfer distances, the coefficients of mass and heat transfer are large. Usually, film coefficients of heat and mass transfer can be estimated using Equations 5.9b and 6.26b, respectively. 

Overall Coefficients. Often overall coefficients of heat and mass transfer are available, rather than the film coefficients used eadier. In that case equation 35 can be rewritten as... 

On the theoretical side, Dmitriev and Bonchkovskaya (D8) have shown that in principle turbulence should spread from waves. Kapitsa (K9) has calculated a general tensor quantity, termed the coefficient of wavy transfer, which is applicable to any flow with periodic disturbances, such as pulsations or surface waves. This treatment predicts an appreciable increase in the rates of heat and mass transfer in wavy films, though this increase does not appear to be as large as that observed experimentally under certain conditions. 

Ponter, A. B. and Au-Yeung, P. H., Estimating Liquid Film Mass Transfer Coefficients in Randomly Packed Columns, in Handbook of Heat and Mass Transfer, Cheremisinoff, N. P. (Ed.), Gulf Publishing Corp., Houston, TX, Chap. 20, Vol. II, pp. 903-952, 1986. 

An air stream at approximately atmospheric temperature and pressure and containing a low concentration of carbon disulphide vapour is flowing at 38 m/s through a series of 50 mm diameter tubes. The inside of the tubes is covered with a thin film of liquid and both heat and mass transfer are taking place between the gas stream and the liquid film. The film heat transfer coefficient is found to be 100 W/mzK. Using a pipe friction chan and assuming the tubes to behave as smooth surfaces, calculate ... 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

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... 

Information recently released (14) shows that the double effect air conditioning version of Rotex has achieved a coefficient of performance of 1.0 at a temperature lift of 35°C using lithium bromide solution. This unit is about to enter field trials. Its high performance is entirely due to the intensity of the heat and mass transfer environment generated on the liquid film flowing over the discs. 

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. 

The amount of additional information needed to be able directly to take into account heat and mass transfer in Model 4 is high. Using the two-film theory, information on the film thickness is needed, which is usually condensed into correlations for the Sherwood number. That information was not available for Katapak-S so that correlations for similar non-reactive packing had to be adopted for that purpose. Furthermore, information on diffusion coefficients is usually a bottleneck. Experimental data is lacking in most cases. Whereas diffusion coefficients can generally be estimated for gas phases with acceptable accuracy, this does unfortunately not hold for liquid multicomponent systems. For a discussion, see Reid et al. [8] and Taylor and Krishna [9]. These drawbacks, which are commonly encountered in applications of rate-based models to reactive separations, limit our ability to judge their value as deviations between model predictions and experimen-... 

Blasco and Alvarez [28] and Alvarez and Blasco [29] considered the application of flash drying to moisture removal of fish and soya meals. Heat, momentum, aud mass balauce equations were formulated. The model was solved numerically with appropriate coefficients of convective heat and mass transfer. Dilute phase transport of homogeneous radial mono-size particle distribution was considered. The conveying superheated steam was assumed to be an ideal gas. The initial period for heating the particles, during which condensation takes place, was neglected. Using the film theory [30], the effect of the mass transfer on the heat transfer coefficient... 

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