Membrane-based total heat exchanger is a device to recover both sensible heat and moisture from exhaust air stream from a building. Heat and mass transfer intensification has been undertaken by using a structure of cross-corrugated triangular ducts. To further intensify moisture transfer, recently developed membranes-one step made asymmetric membranes, are used as the exchanger materials. Conjugate heat and mass transfer under transitional flow regime in this total heat exchanger are investigated. Contrary to the traditional methods of assuming a uniform temperature (concentration) or a uniform heat flux (mass flux) boundary condition, in this study, the real boundary conditions on the exchanger surfaces are obtained by the numerical solution of the coupled equations that govern the transfer of momentum, energy and moisture in the two air streams and in the membrane materials. The naturally formed heat and mass boundary conditions are then used to calculate the local and mean Nusselt and Sherwood numbers along the exchanger ducts, in the heat and mass developing regions. The data are compared with those results under uniform temperature (concentration) and uniform heat flux (mass flux) boundary conditions, for cross-corrugated triangular ducts with typical duct apex angles of 60 degrees and 90 degrees. (C) 2015 Elsevier Ltd. All rights reserved.