In this study, a numerical analysis of turbulent flow heat and mass transfer in the cross-flow transport membrane condenser (TMC) based heat exchange was carried out. The heat exchanger under investigation was designed to recover both sensible and latent heat due to transport of heat and mass through a nanoporous ceramic membrane in the bundle of tubes of the heat exchanger. The shear stress transport SST k-ω turbulence model was used to model the turbulent flow of the flue gas mixture. The condensation rate of the water vapor from the flue gas were calculated using a mixed condensation model. The mixed model was based on the capillary condensation and wall condensation in the membrane tube. The numerical study was focused on the investigation of the impact of the turbulence intensity of the flue gas at various inlet conditions, such as Reynolds numbers and temperatures, on the heat and mass transfer and pressure drop characteristics. The numerical results were validated against the experimental results reported in the literature. Different tube diameters were used in the simulation, with the Reynolds number varied from 3000 to 10000. The results showed that an increase in turbulence intensity led to a significant increase in the turbulent kinetic energy, condensation rate, average convective Nusselt number and change on the pressure drop in the heat exchanger. The effects of inlet flow Reynolds number and tube diameter on the heat and mass transfer were also presented and discussed.