In this article, a comprehensive model has been developed for analyzing the transport phenomena in hollow fibre membrane contactors operated under non-wetted or partially wetted conditions. In this regard, the dynamic behaviour of membrane contactors, considering the entrance regions of momentum, thermal energy, and mass transfers, was investigated carefully. Moreover, effects of temperature distribution on the contactor efficiency were examined by taking into account the influences of heat of solution, heat of reaction, and the viscous dissipation. The chemical system studied was a gas sweetening process, including methane and carbon dioxide as the gaseous mixture, and MEA aqueous solution as the solvent. CFD techniques have been used to solve the nonlinear governing equations simultaneously, and the model predictions were validated against reported experimental data in the literature, and excellent agreement was found. Comparing the model predictions with those of previous models shows relatively better accuracy of the model predictions. Furthermore, distributions of velocity, temperature, and species concentrations in the tube side, shell side, and the membrane were obtained and the effects of various operating and design parameters such as wetting fraction, gas and liquid inlet velocities, inlet temperature of the solvent, MEA concentration, and CO2 volume fraction of the feed on these distributions were carefully studied. Finally, the dynamic response of the system was investigated by analyzing the contactor's response to different step and pulse changes.