This work presents a three-dimensional numerical prediction of the current density for a Proton Exchange Membrane Fuel Cell (PEMFC) with a tree-like pattern, which is observed in the nature, for the flow field channels. The numerical model considers a complete solution of the Navier-Stokes Equation, the species transport equation and two potential field equations; the model is solved using a finite volume technique assuming isothermal and steady state conditions. The three-dimensional model includes the analysis of: current collectors, flow channels, gas diffusion layers, catalyst layers on both sides of the PEMFC (anode and cathode) and a membrane between the two catalyst layers. The contours of the current density are compared to other models found in the technical literature. The results of the model presented here show that the average current density is larger than for conventional models (such as serpentine flow paths). This suggests that more efficient flow field paths could be build with this constructal theory-based pattern for the flow field channels.

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