A comprehensive modeling, analysis, and optimization of two phase, non–isobaric, and non–isothermal PEM fuel cell

•Two–phase modeling of PEM–FC, taking into account various phenomena: contact and mass exchange effects between non–isothermal gas and liquid phases, and pressure effects (non-isobaric on the cathode and anode sides);.•Calculating the optimal values of the main geometrical parameters using different optimization methods;.•Providing a comprehensive model to investigate PEM–FC performance to reduce computational costs;.•Decreasing energy generation costs by the PEM–FC using the parameter optimization method. This study models a non-isobaric, non-isothermal two-phase flow in a Polymer Electrolyte Membrane Fuel Cell (PEM-FC), focusing on conservation equations for mass, energy, and momentum across its components. Verification involves comparing PEM-FC performance and temperature distribution with experimental and literature data, showing consistent agreements. Results indicate that increasing cathode channel pressure enhances membrane moisture and reduces power loss. Higher oxygen partial pressure improves PEM-FC performance, whereas increased anode channel pressure heightens ohmic losses and lowers output voltage. Temperature distribution reveals highest temperatures near the cathode catalyst layer due to electrochemical reactions. Adjusting pressures in cathode and anode channels affects these temperatures accordingly. PEM-FC power density is optimized using various algorithms, with simulated annealing proving most effective. Optimal values for gas diffusion layer thickness, electrode porosity, and inlet humidity are determined. Under constant current density, power density increases by 6 % compared to baseline conditions, demonstrating effective parameter optimization for enhancing PEM-FC performance.