Special Issue on Fuel Cells: Modeling, Analysis, and Computation (2009)

As fossil energy resources become scarcer and as the difficult transition to renewable energy unfolds, it is critical that energy conversion devices with the highest efficiencies be chosen. Fuel cells have dramatically higher potential energy conversion efficiencies than Carnot limited heat engines at the moderate temperatures of operation typically used. This is because in a fuel cell, as in a battery, chemical energy is directly converted to electrical energy. Furthermore, because fuel cells store their fuel externally from the device, they have much higher energy densities than batteries with much higher achieved levels of safety. Fuel cells also have potentially longer lifetimes than batteries, depending on how they are operated. Unfortunately, there are still some rather severe limits on fuel cell commercialization above the 10,000 or so units currently being manufactured annually. It is true to say that applied mathematicians and computational scientists could contribute to all the major fuel cell barriers. These primarily concern cost, operational parameters, catalysis, and durability. Low temperature devices based on polymeric proton exchange membranes (PEM) need the PEM to be fully hydrated with liquid water to achieve adequate proton conduction and hence practical power densities. As the fuel cell produces water, this leads to complex water management issues. Furthermore, the low temperature of operation requires very high loadings of platinum to catalyze the oxygen reduction reaction, which is not well understood in terms of the effect of water and of the PEM itself. High temperature fuel cells based on solid oxide conducting ceramics have complex heat management issues on start up and cool down, use rather expensive oxide materials, and face sealing issues if high power densities are to be achieved. Fuel cells based on other electrolytes or even biological systems also have their unique advantages and challenges. It is clear that the subject of fuel cells is important, broad, and truly multidisciplinary. To develop successfully, contributions are needed from a wide range of scientists and engineers. Therefore, it was decided that a special issue of the SIAM Journal on Applied Mathematics, entitled “Fuel Cells: Modeling, Analysis, and Computation,” would be appropriate. The stated goals were to display new research on fuel cells involving applied mathematics, interpreted broadly, and to encourage more activity by mathematical scientists in the modeling, analysis, and understanding of fuel cells. The two editors of the special issue are Paul Martin (an applied mathematician) and Andrew Herring (an applied chemist), both from the Colorado School of Mines, home of the Colorado Fuel Cell Center and the Renewable Energy Materials Research Science and Engineering Center. An open call for papers was issued and all submitted papers were subject to peer review. Authors were encouraged to try to communicate with mathematical scientists who may not be experts on fuel cells. In addition, the first two papers in the special issue give overviews, again with the intention of attracting more workers into the field. We close this short introduction by giving some general references to the science and technology of fuel cells. The definitive reference work is the four-volume set edited by Vielstich, Lamm, and Gasteiger . For a good collection of review articles, see the special issue of Chemical Reviews edited by Whittingham, Savinell, and Zawozinski . O'Hayre et al. have written a good introductory textbook, now in its second edition. The U.S. Department of Energy has a useful website . There are also websites intended for the fuel cell industry . Finally, the Smithsonian Institution has a website dedicated to the history of fuel cells . The editors thank all the authors and reviewers for their contributions to this special issue.