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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.