# Mathematical Modeling of Fuel Cells

Fuel cells are devices that use chemical reactions to generate electricity directly.  They offer a much more efficient means to convert chemical energy to electrical energy (the efficiency can range from 50 to 60 percent in comparison to approximately 30 percent for combustion based power plants) and in certain applications where the waste heat can be used even higher efficiency is possible.

Hydrogen-oxygen fuel cells were used in the Gemini and Apollo spacecrafts to generate power, and, as a byproduct, drinking water.  In more recent news, most of the large automakers have fuel cell research programs and prototype fuel cell powered vehicles.  Methanol powered fuel cells are under development by a number of companies to power portable electronic devices.  IBM and Sanyo, for example, have announced plans to develop fuel cells to power laptop computers, and Toshiba has already announced plans to commercialize the world's smallest methanol fuel cell.

After decades of research and development by companies large and small, as well as government and academics labs, what is there left to do?  Lots!  Hydrogen-oxygen fuel cells are complicated devices.  A description of these devices involves electrochemistry as well as multiphase and multi-component heat and mass transfer with the possibility of phase changes, in a highly anisotropic porous medium.  (And this is only a part of the problem!)  We'll explore the possibility of using mathematics to simplify some of these complicated models, and show how doing this can help with the interpretation of experimental data as well as with experimental designs.

Journal References:

D. Natarajan and T.V. Nguyen. A two-dimensional two-phase, multi-component, transient model for the cathode of a proton exchange membrane fuel cell using conventional gas distributors, Journal of the Electrochemical Society, 148: A1324-A1335, 2001.

U. Pasaogullari and C.Y. Wang. Liquid water transport in gas diffusion layer of polymer electrolyte fuel cells, Journal of the Electrochemical Society, 151: A399-A406, 2004.

Web Reference:

http://www.howstuffworks.com/fuel-cell.htm