Analytical model of a membrane humidifier for polymer electrolyte membrane fuel cell systems

An analytical model for a membrane humidifier is developed for counter-current flow configuration at steady-state, which is applicable to plate-and-frame as well as shell-and-tube humidifiers. For the first time, the dependence of mass transfer on heat transfer is incorporated in the analytical model and analytical expressions are obtained for the temperature, H2O concentration and water transfer rate. It is shown that neglecting the effect of mass transfer on heat transfer can result in errors in the predicted temperature and relative humidity. Sensitivity analysis was performed to study the effect of design variables and operating conditions on the humidifier performance. The model predictions were found to be consistent with the literature experimental data for a wide range of operating conditions. Simulations were performed to analyze a system consisting of a humidifier and a fuel cell stack. It was found that high current densities resulted in high water transfer rates but decreased relative humidity at the stack inlet. High operating pressure improved the performance of the humidifier, however, at the cost of increased parasitic losses in the system. The relative humidity at the dry side outlet was found to be dominated by the dry side operating conditions while the water transfer rate and humidifier efficiency were found to be dominated by the wet side operating conditions.