迴流的裝置在許多的化工程序中對操作方面有著明顯且重要的影響，例如在氣升式反應器或蒸餾塔加入迴流裝置可提高熱傳或質傳效率。本研究是設計圓形管加裝一可滲透且忽略厚度之薄膜，使之成為一組外管壁於正弦質量通量(Sinusoidal wall fluxes)且具有迴流裝置之圓柱同心套管質量交換器。經由質量守恆所推導出的數學模型會產生一組共軛偏微分方程式，利用弗賓納斯(Frobenius)法來求得其近似解後，可獲得其管內濃度分佈及謝塢數(Sherwood number)。本研究探討迴流效應對圓柱同心套管間的質傳效率之影響，再將其結果與單行程質量傳送系統作比較，以驗證二行程系統的質傳提升率。結果顯示，本系統在格拉茲數大時，其效率提昇率有明顯改善，而不同的薄膜位置對質傳效率有較顯著影響。譬如，在本文二行程中，內管進外管出之無迴流模型，當薄膜位置愈接近外管壁時，有最佳的質傳效率。 A new double-pass mass exchanger with sinusoidal wall fluxes is obtained by inserting a permeable membrane into a circular tube. The device with recycle operation is developed in this study to improve the device performance. The resultant mathematical formulation of such double-pass devices was derived theoretically and the approximation solution was obtained by using the orthogonality principle and Frobenius method. The concentration distribution and mass transfer efficiency were represented graphically, and compared with those in single-pass devices of the same working dimensions. The theoretical predictions show that the considerable improvement of the device performance is obtainable by introducing recycle-effect concept for conducting double-pass operations. The effects of permeable-barrier position and recycle ratio on the mass transfer efficiency as well as on the of power consumption increment have also been discussed.