Mass transfer pipe flow

Note Equation (4.241) characterizes diffusion when the mixture element is in steady state with no turbulence. Diffusion in a pipe can be represented by Eq. (4.241) in convective mass transfer the flow and turbulence are important. 

Mass transfer for flow inside wetted-wall towers. When a gas is flowing inside the core of a wetted-wall tower the same correlations that are used for mass transfer of a gas in laminar or turbulent flow in a pipe are applicable. This means that Eqs. (7.3-24) and (7.3-25) can be used to predict mass transfer for the gas. For the mass transfer in the liquid film flowing down the wetted-wall tower, Eqs. (7.3-22) and (7.3-23) can be used for Reynolds numbers of 4T/p as defined by Eq. (2.9-29) up to about 1200, and the theoretically predicted values should be multiplied by about 1.5 because of ripples and other factors. These equations hold for short contact times or Reynolds numbers above about 100 (SI). 

TABLE 5-23 Mass-Transfer Correlations for Flow in Pipes and Duets—Transfer is from Wall to Fluid... 

In addition to momentum, both heat and mass can be transferred either by molecular diffusion alone or by molecular diffusion combined with eddy diffusion. Because the effects of eddy diffusion are generally far greater than those of the molecular diffusion, the main resistance to transfer will lie in the regions where only molecular diffusion is occurring. Thus the main resistance to the flow of heat or mass to a surface lies within the laminar sub-layer. It is shown in Chapter 11 that the thickness of the laminar sub-layer is almost inversely proportional to the Reynolds number for fully developed turbulent flow in a pipe. Thus the heat and mass transfer coefficients are much higher at high Reynolds numbers. 

For flow in a smooth pipe, the friction factor for turbulent flow is given approximately by the Blasius equation and is proportional to the Reynolds number (and hence the velocity) raised to a power of -2. From equations 12.102 and 12.103, therefore, the heat and mass transfer coefficients are both proportional to w 75. 

The application of the analogies to the problems of heat and mass transfer to plane surfaces and to pipe walls for fully developed flow is discussed later. 

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 ... 

Calame JP, Myers RE, Binari SC, Wood FN, Garven M (2007) Experimental investigation of micro-channel coolers for the high heat flux thermal management of GaN-on-SiC semiconductor devices. Int J Heat Mass Transfer 50 4767-4779 Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single- phase flow in capillary pipes. Exp Thermal Fluid Sci 28 87-95 Celata GP (2004). Heat transfer and fluid flow in micro-channels. Begell House, N.Y. 

Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16 359-368... 

Zhao TS, Bi QC (2001b) Pressure drop characteristics of gas-liquid two-phase flow in vertical miniature triangular channels. Int J Heat Mass Transfer 44 2523-2534 Zimmerman R, Gurevich M, Mosyak A, Rozenblit R, Hetsroni G (2006) Heat transfer to air-water annular flow in a horizontal pipe. Int J Multiphase Flow 32 1-19... 

In the second example, let the case of forced convective mass transfer in pipe flow be considered. Let it be assumed that the turbulent flow of the fluid, B, through the pipe is accompanied by a gradual dissolution of the material, A, of the pipe wall. Experimental... 

Thus, the case of forced convective mass transfer in pipe flow, one has Sh — f (Re, Sc)... 

For flow parallel to an electrode, a maximum in the value of the mass-transfer rate occurs at the leading edge of the electrode. This is not only the case in flow over a flat plate, but also in pipes, annuli, and channels. In all these cases, the parallel velocity component in the mass-transfer boundary layer is practically a linear function of the distance to the electrode. Even though the parallel velocity profile over the hydrodynamic boundary layer (of thickness h) or over the duct diameter (with equivalent diameter de) is parabolic or more complicated, a linear profile within the diffusion layer (of thickness 8d) may be assumed. This is justified by the extreme thinness of the diffusion layer in liquids of high Schmidt number ... 

Of considerable interest is the use of small isolated electrodes, in the form of strips or disks embedded in the wall, to measure local mass-transfer rates or rate fluctuations. Mass-transfer to spot electrodes on a rotating disk is represented by Eqs. (lOg-i) of Table VII. Analytical solutions in this case have to take account of curved streamlines. Despic et al. (Dlld) have proposed twin spot electrodes as a tool for kinetic studies, similar to the ring-disk electrode applications of disk and ring-disk electrodes for kinetic studies are discussed in several monographs (A3b, P4b). In fully developed channel or pipe flow, mass transfer to such electrodes is given by the following equation based on the Leveque model ... 

By substituting the well-known Blasius relation for the friction factor, Eq. (45) in Table VII results. Van Shaw et al. (V2) tested this relation by limiting-current measurements on short pipe sections, and found that the Re and (L/d) dependences were in accord with theory. The mass-transfer rates obtained averaged 7% lower than predicted, but in a later publication this was traced to incorrect flow rate calibration. Iribame et al. (110) showed that the Leveque relation is also valid for turbulent mass transfer in falling films, as long as the developing mass-transfer condition is fulfilled (generally expressed as L+ < 103) while Re > 103. The fundamental importance of the Leveque equation for the interpretation of microelectrode measurements is discussed at an earlier point. 

In 1962 Jottrand and Grunchard (J7) reported on mass transfer to a small rectangular nickel plate immersed in a liquid fluidized bed of sand particles. Mass-transfer rates were five to ten times higher than those measured in an open pipe flow a maximum rate was measured at a bed porosity of 0.58. Le Goff et al. (Lie) later showed that this maximum is directly related to a maximum in the average kinetic energy of the fluidized particles per unit bed volume. 

In order to investigate the dependence of a fast reaction on the nature of the metal, Iwasita et al. [3] measured the kinetics of the [Ru(NH,3)6]2+/3+ couple on six different metals. Since this reaction is very fast, with rate constants of the order of 1 cm s-1, a turbulent pipe flow method (see Chapter 14) was used to achieve rapid mass transport. The results are summarized in Table 8.1 within the experimental accuracy both the rate constants and the transfer coefficients are independent of the nature of the metal. This remains true if the electrode surfaces axe modified by metal atoms deposited at underpotential [4]. It should be noted that the metals investigated have quite different chemical characteristics Pt, and Pd are transition metals Au, Ag, Cu are sd metals Hg and the adsorbates T1 and Pb are sp metals. The rate constant on mercury involved a greater error than the others... 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

For mass transfer in two-component cocurrent two-phase flow, very little work seems to have been carried on in systems analogous to those for which pressure-drops have been measured, that is, in tubes, pipes, or rectangular channels. Only two publications dealing with vertical flow (V2, V3), and two concerned with horizontal flow (A5, S6), have appeared. 

Stirred tank reactors (STR) are the most frequently used reactors in lab-scale ozonation, partially due to the ease in modeling completely mixed phases, but they are very seldom used in full-scale applications. There are various modifications with regard to the types of gas diffusers or the construction of the stirrers possible. Normally lab-scale reactors are equipped with coarse diffusers, such as a ring pipe with holes of 0,1-1.0 m3 diameter. The k/ a-values are in the range of 0.02 to 2.0 s (see Table 2-4 ), which are considerably higher than those of bubble columns. From the viewpoint of mass transfer, the main advantage of STRs is that the stirrer speed can be varied, and thus also the ozone mass transfer coefficient, independently of the gas flow rate. 

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