A simple, mathematical model of thermal coupling in fuel cell stacks

The authors develop a model of steady state thermal transfer in polymer electrolyte membrane fuel cell stacks. The model is appropriate for straight coolant channel unit cell designs and considers quantities averaged over the cross-channel direction, ignoring the impact of the gas and coolant channel geometries. At steady state and under the assumption that the membrane and electrodes are infinitesimally thin, a simple description can be made of the temperature distribution in the cells. The model provides estimates on two important quantities: the local temperature difference between coolant and membrane, and the spread of heat from an anomalously hot cell to its neighbours in a stack environment. The former question is easy to address after the model is presented. The latter requires small argument Laplace transform asymptotics that correspond to a large scaled heat transfer coefficient to the coolant channels. Results of computational approximation of the model are also shown and compared to the asymptotics.