This paper presents a two-dimensional heat and mass transfer model for proton-exchange-membrane (PEM) fuel cells, focusing on water and heat management. The model accounts for water transport across the membrane by electro-osmosis and diffusion, heat transfer from the solid phase to the gas phase, and latent heat associated with water evaporation and condensation in the flow channels. The study highlights that at high current densities (>4 A/cm²), the membrane is not sufficiently hydrated, leading to increased ohmic losses. To minimize these losses, the anode stream must be humidified, and when air is used instead of pure oxygen, the cathode stream also needs to be humidified. The model evaluates four humidification designs: conventional, vapor injection, external humidification, and liquid injection. The results show that the liquid injection design, which involves injecting additional liquid water into the fuel cell, performs better than the conventional design, maintaining higher ionic conductivity and cell voltage. Additionally, the study demonstrates that using air instead of pure oxygen requires humidifying both the anode and cathode streams to prevent membrane dehydration. The model can be used to optimize heat removal and humidification strategies for PEM fuel cells, enhancing their performance and energy efficiency.This paper presents a two-dimensional heat and mass transfer model for proton-exchange-membrane (PEM) fuel cells, focusing on water and heat management. The model accounts for water transport across the membrane by electro-osmosis and diffusion, heat transfer from the solid phase to the gas phase, and latent heat associated with water evaporation and condensation in the flow channels. The study highlights that at high current densities (>4 A/cm²), the membrane is not sufficiently hydrated, leading to increased ohmic losses. To minimize these losses, the anode stream must be humidified, and when air is used instead of pure oxygen, the cathode stream also needs to be humidified. The model evaluates four humidification designs: conventional, vapor injection, external humidification, and liquid injection. The results show that the liquid injection design, which involves injecting additional liquid water into the fuel cell, performs better than the conventional design, maintaining higher ionic conductivity and cell voltage. Additionally, the study demonstrates that using air instead of pure oxygen requires humidifying both the anode and cathode streams to prevent membrane dehydration. The model can be used to optimize heat removal and humidification strategies for PEM fuel cells, enhancing their performance and energy efficiency.