A water and heat management model for proton-exchange-membrane (PEM) fuel cells was developed to investigate the effectiveness of various humidification designs. The model accounts for water transport across the membrane via electro-osmosis and diffusion, heat transfer between solid and gas phases, and latent heat associated with water evaporation and condensation. Results show that at high current densities (>1 A/cm²), ohmic losses in the membrane account for a large fraction of voltage loss, and back diffusion of water from the cathode side is insufficient to maintain membrane hydration. Therefore, the anode stream must be humidified, and when air is used instead of pure oxygen, the cathode stream must also be humidified. PEM fuel cells are promising for terrestrial applications due to their simplicity and low-temperature operation. Recent improvements in catalyst loading, membrane conductivity, and cost reduction have increased their attractiveness. However, achieving high power density and energy efficiency remains a challenge. Proper water and heat management is essential for high power density performance at high energy efficiency, as it helps maintain membrane hydration and conductivity, reducing ohmic losses and increasing cell voltage. The model is a steady-state, two-dimensional heat and mass-transfer model of a PEM fuel cell. It considers water and gas transport across the membrane and along flow channels, and heat transfer between solid phases and gases. The model assumes uniform solid temperatures, plug-flow conditions, constant total pressure, negligible gas-phase conduction, and other simplifications. The model accounts for water transport, including condensation and evaporation, and uses equations to calculate the electro-osmotic coefficient and diffusion coefficient of water in the membrane based on water activity in the gas phase. The model was used to evaluate the effectiveness of three humidification strategies and the effect of air operation. Results show that back diffusion of water from the cathode to the anode is insufficient to maintain membrane hydration at high power densities and energy efficiency. Therefore, the anode gas stream must be humidified. When air is used, the cathode stream must also be humidified. The model can be used as a design tool to evaluate the effectiveness of various heat removal and humidification designs and the effects of design and operating parameters on PEM fuel cell performance.A water and heat management model for proton-exchange-membrane (PEM) fuel cells was developed to investigate the effectiveness of various humidification designs. The model accounts for water transport across the membrane via electro-osmosis and diffusion, heat transfer between solid and gas phases, and latent heat associated with water evaporation and condensation. Results show that at high current densities (>1 A/cm²), ohmic losses in the membrane account for a large fraction of voltage loss, and back diffusion of water from the cathode side is insufficient to maintain membrane hydration. Therefore, the anode stream must be humidified, and when air is used instead of pure oxygen, the cathode stream must also be humidified. PEM fuel cells are promising for terrestrial applications due to their simplicity and low-temperature operation. Recent improvements in catalyst loading, membrane conductivity, and cost reduction have increased their attractiveness. However, achieving high power density and energy efficiency remains a challenge. Proper water and heat management is essential for high power density performance at high energy efficiency, as it helps maintain membrane hydration and conductivity, reducing ohmic losses and increasing cell voltage. The model is a steady-state, two-dimensional heat and mass-transfer model of a PEM fuel cell. It considers water and gas transport across the membrane and along flow channels, and heat transfer between solid phases and gases. The model assumes uniform solid temperatures, plug-flow conditions, constant total pressure, negligible gas-phase conduction, and other simplifications. The model accounts for water transport, including condensation and evaporation, and uses equations to calculate the electro-osmotic coefficient and diffusion coefficient of water in the membrane based on water activity in the gas phase. The model was used to evaluate the effectiveness of three humidification strategies and the effect of air operation. Results show that back diffusion of water from the cathode to the anode is insufficient to maintain membrane hydration at high power densities and energy efficiency. Therefore, the anode gas stream must be humidified. When air is used, the cathode stream must also be humidified. The model can be used as a design tool to evaluate the effectiveness of various heat removal and humidification designs and the effects of design and operating parameters on PEM fuel cell performance.