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PEM fuel cells: a mathematical overview. (English) Zbl 1189.35002

Summary: We present an overview of the mathematical issues that arise in the modeling of polymer electrolyte membrane fuel cells. These issues range from nanoscale modeling of network structures arising in pore formation within the polymer and the formation of nanostructured agglomerates within the catalyst layer, to macroscale models of multiphase flow and water management, degradation of catalyst layers and membrane, and development of stack level codes. The dominant themes are the development and analysis of multiscale models and their reduction to simplified forms that are implementable in stack-level computations.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35M10 PDEs of mixed type
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
49S05 Variational principles of physics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76T30 Three or more component flows
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