The longitudinal fluid flow and heat transfer between an elliptical hollow fiber membrane tube bank (EHFMTB) used for air humidification are investigated. In the tube bank, the water stream flows inside the fibers, while the air stream flows axially between the fibers. The air and the water streams, in a counter flow arrangement, are exchanging heat and moisture effectively through the membranes. Two regularly populated arrangements of the tube bank, in-line and staggered, are considered. Two representative unit cells consisting of two fibers and the air stream flowing longitudinally between the fibers are selected as the calculation domains. The governing equations for the fluid flow and the heat transfer between the EHFMTB are established and numerically solved via a boundary-fitted coordinate transformation method. The friction factor and Nusselt number in the unit cells are then obtained, analyzed, and experimentally validated. They are compared with the data obtained for a hollow fiber membrane tube bank (HFMTB). The results are useful for structural optimization and performance evaluations of the EHFMTB employed for air humidification. (C) 2013 Elsevier Ltd. All rights reserved.