In this paper, a numerical study has been carried out to investigate the heat and mass transfer characteristics of a condensing combustion flue gas in a cross-flow transport membrane tube bundle. The tube wall is made of a porous material that is able to extract condensate liquid from the flue gas. The flue gas investigated consists of one condensable water vapor (H2O) and three noncondensable gases (CO2, O-2, and N-2). A simplified multi-species transport model was developed for the heat and mass transfer of flue gas. The condensation-evaporation process was simulated as a two-step chemical reaction. The RNG two-equation turbulence model was used for the turbulent flow. The numerical study was conducted within ranges of Reynolds number of 1.0 x 10(3)-7 x 10(4) based on hydraulic diameter of flue gas channel, and 6.4 x 10(0)-3.3 x 10(2) based on inner diameter of the water tube. Flue gas inlet temperature is within the range of 333.2-360.9 K. Numerical results were compared with our experimental data. It has been found that the developed multi-species transport model was able to predict the flue gas heat and mass transfer in the tube bundle with fairly good accuracy. The heat and mass depletion levels decrease with the increase of the flue gas Reynolds numbers. A new Nusselt number correlation was developed for flue gas convection in the tube bundle. Detailed results about temperature, mass fraction, enthalpy, and skin fraction factors are also presented and discussed. (C) 2012 Elsevier Ltd. All rights reserved.