An approximate analytical solution to channel flow in a fuel cell with a draft angle

This paper investigates the channel flow with a suction or injection boundary condition to imitate the reactant flow in fuel cells. A two-dimensional model is proposed for a channel with a trapezoidal cross-section, and systematically analyzed using the perturbation method and the Laplace transform technique. The model predicts the species concentration at the electrode of the fuel cell under the constraint of uniform current density along the channel. For convenience of use as a formula, the asymptotic solutions to some results are found for two different limits of x/k.