A new device of multi-pass mass,exchanger was developed by inserting three idealized membranes to divide an open conduit into four sub-channels. The mathematical formulations of the device with external recycle, as referred to a well-known conjugated Graetz problem, were conducted to improve the mass transfer efficiency. The eigenfunction expansion technique with the eigenfunction expanding in terms of an extended power series was used to solve such a conjugated Graetz problem analytically. The theoretical predictions were presented graphically and compared with those in the single-pass operations (without any idealized membrane inserted and external recycle) of the same working dimensions.