Seeking minimum entropy production for a tree-like flow-field in a fuel cell

Common for tree-shaped, space-filling flow-field plates in polymer electrolyte fuel cells is their ability to distribute reactants uniformly across the membrane area, thereby avoiding excess concentration polarization or entropy production at the electrodes. Such a flow field, as predicted by Murray's law for circular tubes, was recently shown experimentally to give a better polarization curve than serpentine or parallel flow fields. In this theoretical work, we document that a tree-shaped flow-field, composed of rectangular channels with T-shaped junctions, has a smaller entropy production than the one based on Murray's law. The width w0 of the inlet channel and the width scaling parameter, a, of the tree-shaped flow-field channels were varied, and the resulting Peclet number at the channel outlets was computed. We show, using 3D hydrodynamic calculations as a reference, that pressure drops and channel flows can be accounted for within a few percents by a quasi-1D model, for most of the investigated geometries. Overall, the model gives lower energy dissipation than Murray's law. The results provide new tools and open up new possibilities for flow-field designs characterized by uniform fuel delivery in fuel cells and other catalytic systems.