Boundary conditions for asymmetric wall heat fluxes in double-pass parallel-plate laminar countercurrent operations are analyzed theoretically in this work by using an eigenfunction expansion in terms of power series for the homogeneous part and an asymptotic solution for the non-homogeneous part. Effects of variable ratio of heat fluxes on both sides and impermeable-sheet location are also studied. Quantitative and qualitative interpretations of theoretical predictions are utilized to investigate of heat-transfer efficiency enhancement of the double-pass model under consideration as compared to those in the single-pass operations without an impermeable sheet inserted. Results are presented in terms of Nusselt number and device performance improvement. The influence of the impermeable-sheet location on the heat-transfer efficiency enhancement as well as on the power consumption increment in double-pass operations has also been delineated. (C) 2009 Elsevier Ltd. All rights reserved.