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An optimum humidification of the reactant gases of proton exchange membrane (PEM) fuel cell extremely affects its performance. Here, an analytic model of a membrane humidifier for PEM fuel cell is proposed where the effect of mass flow rates, inlet temperatures and pressures are investigated. The governing equations: water transfer equation and the law of conservation of energy in whole humidifier are written, which form a Non-linear system of equations, solved through FORTRAN software. At each stage, the outlet temperatures, the water transfer rate, relative humidity and the dew point at dry side outlet are calculated and discussed. The closer the dry side outlet dew point to the wet side inlet dew point, leads to the better humidifier performance. The results show that an increase in mass flow rate at dry side inlet leads to the weaker humidifier performance; while, an increase in mass flow rate at wet side inlet leads to the better performance. An increase in the pressure at dry side inlet enhances humidifier performance; while, the pressure at wet side inlet does not affect significantly on humidifier performance. Here, preheating the dry gas is not essential and use the cooler wet gas is recommended

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Reactant gases should be humidified before entering a polymer electrolyte membrane (PEM) fuel cell stack. Humidification of the gases can be performed by a membrane humidifier. In the present study, an analytical model has been proposed to investigate the performance of a water-gas membrane humidifier which is used in the fuel cell systems. At first, a set of nonlinear equations was obtained by applying the mass and energy conservation laws on the gas side of the humidifier. The temperature and the humidity ratio of the outlet gases from the humidifier are the unknowns of these nonlinear equations. The proposed model can evaluate the performance of the humidifier based on the temperature and relative humidity of the outlet gases from the humidifier. The effects of different parameters like: gas flow rate, channel's length and depth, temperature and pressure of the inlet gases on the performance of the humidifier were studied by the developed model. The results show that the channel depth does not have an effect on the temperature and humidity of the humidified outlet gases. In addition, increasing the channel length causes an increase on the dew point of the outlet gases but the relative humidity of the dry inlet gas does not have a noticeable effect on the dew point of the outlet gases. Increasing the temperature of the inlet gases cannot improve the humidifier performance, considerably. The results of the model show that increasing the inlet pressure and using less air flow improve the humidifier performance.

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Using the renewable energy resources has attracted the attention of researchers and automobile companies, because of limited fossil fuel resources, low efficiency of internal combustion engines and their environmental pollutions. By using the fuel cell systems instead of internal combustion engines can be partially overcome these problems. In this regard, the present article examines a PEM fuel cell system for using in an urban vehicle. In the first part of this article, by using the real component of system, the fuel cell system components including stack, membrane humidity of air and hydrogen, air compressor, water pump and pump cooler stack has been modeled in MATLAB Simulink environment. The mentioned model can evaluate the power consumption of system and its peripheral component and also required water, hydrogen and air for system. At the base case and the current density of 0.7A / cm2, 14% of power productions of stack are consumed by auxiliaries units. At this current density, the overall and net system efficiencies are 48.15% and 34.3%. In the second part of this article, the system from the point of view of the first law of thermodynamics has been optimized with objective functions of maximum output power and maximum efficiency. The results indicate that first model search method is best method for optimization, second at the Optimization with the aim of maximum power, pure power and system efficiency are increased 11.9% and 4% respectively and the power consumption by auxiliary unit is reduced 42%.