Mass transfer high flux, effect

T. A. Peters, M. Stange, H. Klette and R. Bredesen, High pressure performance of thin Pd-23%Ag/stainless steel composite membranes in water gas shift gas mixtures influenee of dilution, mass transfer and surface effects on the hydrogen flux, J. Membr. Sci., 2008, 316, 119-127. 

The equilibrium phosphate program is confined to those utility boilers operating under knife-edge control, where any changes in heat and mass transfer patterns at boiler surfaces and other high-heat flux areas may exert significant ripple effects throughout the boiler plant. 

Mudawar I, Bowers MB (1999) Ultra-high critical heat flux (CHF) for subcooled water flow boiling. I CHF data and parametric effects for small diameter tubes. Int J Heat Mass Transfer 42 1405-1428... 

This effect, usually known as feed-side concentration polarization, may become particularly relevant for solutes with a high sorption affinity towards the membrane, which may lead to its depletion near the membrane interface if external mass-transfer conditions are not sufficiently good to guarantee their fast transport from the bulk feed to the interface [32, 36] (see Figure 11.3). As a consequence of their depletion near the interface the driving force for transport, and the resulting partial fluxes, become lower. 

Complete membrane systems can be operated in a variety of modes with e.g. CO- or counter flow of feed (high pressure side) and permeate (low pressure side) streams and with membrane modules coupled in different ways. Permeation and separation in these complex engineering systems will not be treated in this chapter. Heat and mass transfer limitations on the gas-membrane surfaces or interfaces can be important with high fluxes and/or strongly adsorbing gases as well as in membrane reactors. These effects will not be treated explicitly but are introduced in experimental results, e.g., by variation of sweep rates of permeated gases. 

The next step is to compute the multicomponent mass transfer coefficients modified for the effect of a nonzero total flux. The total mass flux is needed for the evaluation of the high flux correction factor and is... 

Equation (2,4-3) is applicable regardless of the magnitude of the flux so it may he employed to demonstrate the effect of high mass flux. For any ralio of NJNB as NA + NB - 0, the mass transfer coefficients kr and k approach DjJCth. If D CIl is desigaaled as fc°. the coefficient under low transfer tales, an expression for the effect of total mass transfer flux on the ratio A can be derived,... 

A significant criticism of the above model is thei the high mass transfer flux should influence the effective Aim thickness, yet no allowance has been utede for this in tbe film thsory model. A boundary layer model to he described shortly allows for the effect of the high flux On hydrodynamics. 

Many numerical and series solutions for the laminar boundary layer model of mass transfer are available for situations such as flow in coeduits under conditions of fully developed or developing concentration or velocity profiles. Skellaed31 provides a particularly good summary of these results. The laminar boundary layer model has been extended to predict tha effects of high mass transfer flux on the mass transfer coefficient from a flat plate. The results of this work ate shown in Fig. 2.4-2 and. in com rest to the other theories, iedicate a Schmith number dependence of Ihe correction factor. 

At high enough qualities and mass fluxes, however, it would be expected that the nucleate boiling would be suppressed and the heat transfer would be by forced convection, analogous to that for the evaporation for pure fluids. Shock [282] considered heat and mass transfer in annular flow evaporation of ethanol water mixtures in a vertical tube. He obtained numerical solutions of the turbulent transport equations and carried out calculations with mass transfer resistance calculated in both phases and with mass transfer resistance omitted in one or both phases. The results for interfacial concentration as a function of distance are illustrated in Fig. 15.112. These results show that the liquid phase mass transfer resistance is likely to be small and that the main resistance is in the vapor phase. A similar conclusion was reached in recent work by Zhang et al. [283] these latter authors show that mass transfer effects would not have a large effect on forced convective evaporation, particularly if account is taken of the enhancement of the gas mass transfer coefficient as a result of interfacial waves. 

When mass-transfer rates are moderate to high, an additional correction term is needed in equations (6-101) and (6-102) to correct for distortion of the composition profiles. This correction, which can have a serious effect on the results, is discussed in detail by Taylor and Krishna (1993). An alternative approach would be to numerically solve the Maxwell-Stefan equations, as illustrated in Examples 1.17 and 1.18. The calculation of the low mass-transfer fluxes according to equations (6-94) to (6-104) is illustrated in the following example. 

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