Analytical model for magnetic field assisted proton exchange membrane water electrolysis

Proton Exchange Membrane (PEM) water electrolysis is a key pathway for sustainable hydrogen production, yet its performance remains constrained by mass transport and interfacial limitations. Recent studies suggest that external magnetic fields can enhance electrolysis efficiency by modifying charge carrier dynamics and fluid motion, but the contribution of the Hall effect in electrolytic systems is poorly understood. In this work, we develop an analytical model that integrates Faraday law, the Butler-Volmer equation, and a Hall voltage formulation. The model captures the coupled influence of magnetohydrodynamic (MHD) forces and Hall-induced potential variations on proton transport, current density, and hydrogen generation. Validation against experimental data confirms excellent agreement (R² > 0.95) across varying flow rates, with fitted parameters revealing that MHD effects dominate fluid motion while the Hall effect plays a secondary but measurable role. The model predicts substantial efficiency gains at low flow rates and high magnetic fields, with hydrogen yield improvements exceeding 150 % under extrapolated conditions. These findings provide actionable guidance for the design of magnetic field assisted electrolyzers with enhanced hydrogen output.