A parallel-plate membrane contactor with side inlets and side outlets has been designed and used for air humidity control. The contactor is comprised of a series of quasi-counter flow parallel-plate membrane channels (QCPMC). The laminar flow and heat transfer in the QCPMC are investigated based on a unit cell including one membrane and half of the channel. The equations governing the momentum and heat transports are established together with a uniform wall temperature boundary condition and numerically solved by a finite volume difference approach. The mean product of friction factor and Reynolds number (fRe) and Nusselt number (Nu(m)) are then obtained and numerically validated by those taken from other well-known publications. Influences of the Reynolds numbers (Re), entrance ratios (x(in)/x(o)), aspect ratios (x(o)/H), and various fluids with different Prandtl numbers (Pr) on the (fRe)(m), and Nu(m) are obtained and analyzed. It can be found that a distinct vortex is generated for the water stream flowing through the QCPMC when the Re is greater than 100. Further, for the same x(o)/H, the Nu(m), of the LiCI stream is the largest, and next the water stream, the least the air stream. (C) 2015 Elsevier Ltd. All rights reserved.