Considerable improvement of heat transfer in laminar counterflow concentric heat exchangers is obtainable by inserting in parallel an impermeable, resistless sheet to divide an open duct into two subchannels for double-pass operations with external refluxes. Efficiency improvement in heat transfer has been investigated analytically by using an orthogonal expansion technique. The results of improvement in heat transfer efficiency are represented graphically and compared with those in a single-pass operation. The influences of improvement-sheet location and reflux ratio on the enhancement of transfer efficiency as well as on the increment of power consumption have been discussed.