Abstarct: Heat transfer and pressure drop are two important parameters in the design of heat exchangers. In the present thesis, energy recovery systems baxsed on membrane have been investigated with the aim of increasing heat transfer and reducing pressure drop. The structure of this type of heat exchanger includes a permeable steam core, two air flow paths and two fans that direct air currents to the core. These systems include a heat and mass transfer mechanism that uses energy difference between two airflows (supply and exhaust air) or in other words, the energy of the airflow is exchanged in the energy recovery system and doesn’t require any external energy. This paper analyzes the numerical study of new membrane such as circular and Congressional circular, using COMSOL Multiphysics. These novel duct structures have been used to improve the performance of the membrane-baxsed heat exchanger. The cross flow design was investigated under summer conditions. In order to reduce the complexity of the channel shape and modeling the smallest part of the channel flow, as well as better and more precise simulation, the converter is divided into ten cycles and the heat transfer is calculated in each cycle, and the average of ten cycles is measured as the heat transfer rate. The results show that the circular membrane with a semicircular profile increases the heat and mass transfer by about 6% and 3%, and the Congressional circular membrane improves pressure drop by about 47% compared to a triangular heat exchanger. After comparing and evaluating the cost-benefit ratio of the four heat exchanger it has been made clear that the total heat exchanger with Congressional circular duct is more effective than another heat exchanger.