Comprehensive Coupled Electrochemical and Thermal Analysis of Proton Exchange Membrane Fuel Cells Under Dynamic Loads

¹ FEMTO-ST Institute, University of Bourgogne Franche-Comté, UTBM, CNRS, Rue Thierry Mieg, 90000 Belfort, France
² Cadi Ayyad University, Faculty of Sciences and Technologies, Laboratory of Mathematics, Artificial Intelligence and Sustainable Technologies (LMAIST), 40000 Marrakesh, Morocco
³ Cadi Ayyad University, Faculty of Sciences Semlalia, Laboratory of Computer Science and Intelligent Systems (LMAIT), 40000 Marrakesh, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 22 May 2026

Abstract

The current work proposes a complete mathematical model of proton exchange membrane fuel cells (PEMFCs) taking into account the processes of electrophysics, thermodynamics, and transients regime. Electrochemical sub-model divides the potential difference into losses according to physical laws governing the process (activation, ohmic, and mass transfer losses). At the same time, an extended thermal model is built, including the heat produced by chemical reactions and losses, sensible heat, latent heat, and convective cooling by the environment. This thermal model is necessary to consider the actual variations in temperature. The model contains elements of non-stationarity, which allows for solving problems associated with rapidly changing loads; the two-layer capacitor model is used to simulate more accurately voltage transients. All the described models have been developed within MATLAB/Simulink. The results of modeling are compared with high-quality experimental data taken from a Ballard Mark V cell. The simulated voltage and temperature profiles match well with the measured ones and this confirms that this configuration is a good representation of the behavior of the PEMFC in real operating conditions and the proposed model can be considered representative.