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This paper presents a review of the mathematical modeling of two types of polymer electrolyte membrane fuel cells: hydrogen fuel cells and direct methanol fuel cells. Models of single cells are described as well as models of entire fuel cell stacks. Methods for obtaining model parameters are briefly summarized, as well as the numerical techniques used to solve the model equations. Effective models have been developed to describe the fundamental electrochemical and transport phenomena occurring in the diffusion layers, catalyst layers, and membrane. More research is required to develop models that are validated using experimental data, and models that can account for complex two‐phase flows of liquids and gases.

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