An internally-cooled parallel-plate membrane contactor has been proposed, designed, and used for liquid desiccant air dehumidification. It is comprised of a series of side in and out parallel-plate membrane channels (QCPMC). The processing air and the liquid desiccant (solution) streams are separated by the membranes. Cooling tubes are installed in the solution channel to take away the absorption heat. The friction factors and heat transfer coefficients in the complex QCPMC with the cooling tubes in the solution side (QCPMCC) are necessary for the structural design and energy analysis. Therefore the laminar flow and heat transfer in the solution channel are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. The momentum and thermal transport governing equations are built up together with a uniform wall temperature boundary condition and solved by a finite volume approach. The mean (fRe) and Nusselt numbers (Nu(m)) are then calculated. Influences of the Reynolds numbers (Re), tube number (N-tube), tube outer diameters (d(outer)), tube arrangements, and connection types of tubes on the (fRe)(m) and Nu(m) are analyzed. It can be found that when d(outer) = 0.003 m, the (fRe)(m) rises with an increase in the N-tube. However the Nu(m) decrease with the N-tube increasing. When N-tube = 4, the (fRe)(m) rise with an increase in the d(outer). However the larger the d(outer) are, the smaller the Nu(m) are. (C) 2016 Elsevier Ltd. All rights reserved.