Relative simplicity of use, no pollutions and high-efficiency are some of the advantages that will make fuel cells one of the best devices for getting electrical energy in the near future. Micro- and mesoscale modeling of fuel cells gives an important perspective about their efficiency and behavior during the energy conversion process. Due to the high cost of carrying out laboratory experiments related to different materials at the micro- and mesoscales, modeling and simulation of the different elements of the fuel cells are a useful approach and a point of departure for the experimental validation.

This paper describes fuel cell modeling starting with the fundamentals, including physical and chemical characteristics of fuel cells, moving to the current state of the study of modeling based on the Lattice Boltzmann Method (LBM). The principal characteristics and elements of the fuel cells are presented in general as well as the main differences between the Proton Exchange Membrane Fuel Cells (PEMFC) and Solid Oxide Fuel Cells (SOFC). Fuel cells have several parts that are modeled on the micro- and mesoscale level. These parts, conditions and governing equations for different transport phenomena are displayed in this manuscript. A detailed description of the main issues, advantages and recent advances related to Lattice Boltzmann Method as a method for modeling several physical processes that take place within fuel cells are presented.

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