Boundary layer theory states that even for fluids of low viscosity the viscous effects cannot be neglected near the surface of a solid boundary, due to high velocity gradients. Using this theory the Navier-Stokes equations can be simplified to a form in which we can derive an analytical solution. The aim of the project is to couple the a priori knowledge of the mathematical theory with the a posteriori knowledge of electrochemical kinetics that occurs during fuel cell operation.
Many engineering models of fuel cells exist which tend to use computational fluid dynamics to solve a series of complex three dimensional partial differential equations. However, little consideration seems to be given about whether the problem has a solution and whether or not that solution is unique, as well as the overall accuracy of such commercial programs at obtaining a solution to these systems. Furthermore, these systems can sometimes be computed without a full set of boundary conditions which produces underdetermined problems which can be shown to have an infinite number of solutions.
Using mathematical theory of fluid dynamics and numerical methods we can simplify the problem of fluid flow and chemical reactions and gain accurate asymptotic solutions to certain regions of the domain. All of this can be done with computational codes which take seconds to produce numerically accurate solutions. Furthermore, full numerical solutions can be obtained with a very high level of computational efficiency. The outputs of mass concentration and its dependence on cell potential can be examined in order to obtain optimal operating conditions for fuel cell performance.