  Progress on the numerical modeling of a prototype fuel cell is reported. Some
known limitations of the previously published Alpha model are addressed, and
the numerical uncertainty due to discretization of the improved model, Beta,
was estimated. In Part 1, the Beta model is compared to Alpha, where
significant albeit small differences are seen. Shortcomings of the improved
model are discussed, paving the way forward, while a discrepancy with previous
results is addressed, further suggesting the use of the Darcy-Brinkman over
Stokes-Darcy formulation for free and porous media flow. Furthermore, a
parametric study is carried out, constraining plausible values of the reaction
rate constants identifying additional opportunities for validation. In Part 2,
a mesh convergence study is carried out to estimate the discretization error of
Beta model. A reduced, proxy geometry and two extrapolation schemes are used to
estimate the exact solution, which is then used to estimate the model's
uncertainty through the Grid Convergence Index framework. Error estimates are
on average $\sim 10\%$ for the flow rate range simulated, larger than
experimental ones available. Results suggest a difficulty in achieving mesh
convergence in fuel cell-like models, even in simpler cases. Caution is thus
suggested during validation or when devising predictions from numerical models.
Finally, given the uncertainties in the numerical data and the available
experimental data, the results lack validation power, highlighting the need for
additional experimental data and improved precision for the numerical data.
