The fluid flow and conjugate heat and mass transfer in a cross-flow hollow fiber membrane contactor are investigated. The shell-and-tube like contactor is used for liquid desiccant air dehumidification, where numerous fibers are packed into the shell and air flows across the fiber bank. To overcome the difficulties in the direct modeling of the whole contactor, a representative cell, which comprises of a single fiber, a liquid solution inside the fiber, and an air stream across the fiber, is selected as the calculation domain. The air stream in the cell is surrounded by an assumed outer free surface. The equations governing the fluid flow and heat and mass transfer in the two cross-flow streams are solved together with the heat and mass diffusion equations in the membrane. The friction factor and the Nusselt and Sherwood numbers on the air and stream sides are then calculated and experimentally validated. (C) 2012 Elsevier Ltd. All rights reserved.