Mass transfer in pipes

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)... 

Example 2.11 Simultaneous Heat and Mass Transfer in Pipe... 

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

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. 

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. 

Quarmby, A. and Anand, R.K. (1969). Axisymmetric turbulent mass transfer in circular pipe tube../. Fluid Mech., 38, 433-455. 

Mass-Transfer Correlations Because of the tremendous im-ortance of mass transfer in chemical engineering, a veiy large num-er of studies have determined mass-transfer coefficients both empirically and theoretically. Some of these studies are summarized in Tables 5-17 to 5-24. Each table is for a specific geometry or type of contactor, starting with flat plates, which have the simplest geometry (Table 5-17) then wetted wall columns (Table 5-18) flow in pipes and ducts (Table 5-19) submerged objects (Table 5-20) drops and... 

V. Gnielinski. New Equations for Heal and Mass Transfer in Turbulent Pipe and Channel Flow. International Chemical Engineering 16 (1976), pp. 359-368. 

Wigley, T.M.L. Brown, M.C. (1971) Geophysical applications of heat and mass transfer in trubulent pipe flow. Boundary Layer Meteorology 1, 300-320. 

An exclusively analytical treatment of heat and mass transfer in turbulent flow in pipes fails because to date the turbulent shear stress Tl j = —Qw w p heat flux q = —Qcpw, T and also the turbulent diffusional flux j Ai = —gwcannot be investigated in a purely theoretical manner. Rather, we have to rely on experiments. In contrast to laminar flow, turbulent flow in pipes is both hydrodynamically and thermally fully developed after only a short distance x/d > 10 to 60, due to the intensive momentum exchange. This simplifies the representation of the heat and mass transfer coefficients by equations. Simple correlations, which are sufficiently accurate for the description of fully developed turbulent flow, can be found by... 

Von Behren et al. (1972) analyzed multicomponent mass transfer in turbulent flow in a pipe. Show that their model is fundamentally incorrect. You may also refer to the paper by Stewart (1973). 

Concentration gradient for mass transfer in a pipe with turbulent flow of gas. 

C. X. Lin, P. Zhang, and M. A. Ebadian, Laminar Forced Convection in the Entrance Region of Helicoidal Pipes, Int. J. Heat and Mass Transfer. In press. 

Y. I. Cho and J. P. Hartnett, Analogy for Viscoelastic Fluids—Momentum, Heat and Mass Transfer in TUrbulent Pipe Flow, Letters in Heat and Mass Transfer (7/5) 339-346,1980. 

P. J. Marto, Rotating Heat Pipes, in D. E. Metzger and N. H. Afgan (eds.), Heat and Mass Transfer in Rotating Machinery, Hemisphere Publishing Corp., New York, pp. 609-632,1984. 

Berger, F.P. and Hau, K.F., 1977, Mass transfer in turbulent pipe flow measured by the electrochemical method. Int. J. Heat and Mass Trans. 20, 11, 1185-1194. 

Figure 4.3-3 illustrates this diagram for parameter allocation, which was created on the basis of numerous diying experiments. A particle s ratio mass transfer for pipe flow can also be used for particulate systems. If the volume fractions for the continuous and the dispersed phase are known, the ratio d / L ) can be calculated and in addition the ratio diameter by length can be determined using Fig. 4.3-3. 

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