A double-pass concentric circular mass exchanger under uniform wall fluxes is produced by inserting a permeable barrier into a circular tube to improve the device performance. The mathematical formulation was developed theoretically for such double-pass, forced-convection, mass-transfer problems which are referred to as conjugated Graetz problems. The analytical solutions are obtained by the linear superposition of an asymptotic solution and a homogeneous solution which are linear in the axial direction and solved with the use of an eigenfunction expansion in a power series. The analytical results show that the mass-transfer rate of a double-pass mass exchanger can be improved compared to that of a single-pass mass exchanger by suitably adjusting the permeable barrier position. Moreover, the ratio of mass-transfer efficiency improvement and power consumption increment is also shown to make good economic sense.