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By solving numerically the continuity mass\u2010conservation equation with the corresponding boundary conditions, the lumen laminar mass\u2010transfer coefficients for both cases are correlated. The correlations greatly improve the calculating accuracy of the overall mass\u2010transfer coefficient and can be used to obtain the lumen mixed\u2010cup concentration by an algebraic equation substituting the partial differential equation. A separation factor m' is introduced to characterize the effect of the operational mode. Calculation results demonstrate that the lumen mass\u2010transfer coefficient is independent of the real lumen and shell concentrations, but it is greatly influenced by m'. The countercurrent mode, compared to the cocurrent mode, provides not only a higher mean driving force, but a higher lumen mass\u2010transfer coefficient. This conclusion is novel and valid for the tube\u2010shell heat or mass\u2010transfer processes and is supported by the experimental data in the literature and our gas membrane separation experiments.<\/jats:p>","DOI":"10.1002\/aic.690430807","type":"journal-article","created":{"date-parts":[[2004,6,23]],"date-time":"2004-06-23T10:49:19Z","timestamp":1087987759000},"page":"1975-1988","source":"Crossref","is-referenced-by-count":27,"title":["Lumen mass transfer in hollow\u2010fiber membrane processes with constant external resistances"],"prefix":"10.1002","volume":"43","author":[{"given":"Yingjie","family":"Qin","sequence":"first","affiliation":[]},{"given":"Joaquim M. 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