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 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.

A brief review of the thermodynamic and fluid dynamic problems related to long-distance liquid flow and signalling in plants is presented. Geometrical parameters of the plant leaf venation are measured and the general relationships between the diameters and lengths of the veins, branching angles at the vein bifurcations, and the corresponding drainage areas are obtained. The same relationships had been obtained before for the bifurcations of the pathways in the arterial and bronchial systems of mammals and humans; tree trunks, branches and roots; and river basins. The identity of the principle of design of the transportation systems in the nature can be understood on the concept of optimal networks that provide liquid delivery at total minimal energy costs. The corresponding models of the optimal vessels and branching systems of vessels with impermeable and permeable walls are presented and discussed.

The fractal-type flow-fields for fuel cell (FC) applications are promising, due to their ability to deliver uniformly, with a Peclet number Pe~1, the reactant gases to the catalytic layer. We review fractal designs that have been developed and studied in experimental prototypes and with CFD computations on 1D and 3D flow models for planar, circular, cylindrical and conical FCs. It is shown, that the FC efficiency could be increased by design optimization of the fractal system. The total entropy production (TEP) due to viscous flow was the objective function, and a constant total volume (TV) of the channels was used as constraint in the design optimization. Analytical solutions were used for the TEP, for rectangular channels and a simplified 1D circular tube. Case studies were done varying the equivalent hydraulic diameter (D_h), cross-sectional area (D_Σ) and hydraulic resistance (D_Z). The analytical expressions allowed us to obtain exact solutions to the optimization problem (TEP→min, TV=const). It was shown that the optimal design corresponds to a non-uniform width and length scaling of consecutive channels that classifies the flow field as a quasi-fractal. The depths of the channels were set equal for manufacturing reasons. Recursive formulae for optimal non-uniform width scaling were obtained for 1D circular D_h -, D_Σ -, and D_Z -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for D_h -, D_Σ -, and D_Z -based 1D models (Cases 4-6). As a reference case, Murray’s law was used for circular (Case 7) and rectangular (Case 8) channels. It was shown, that Dh-based models always resulted in smaller cross-sectional areas and, thus, overestimated the hydraulic resistance and TEP. The D_Σ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The D_Z -based models fitted best to the 3D CFD data. All optimal geometries exhibited larger TEP, but smaller TV than those from Murray’s scaling (reference Cases 7,8). Higher TV with Murray’s scaling leads to lower contact area between the flow-field plate with other FC layers and, therefore, to larger electric resistivity or ohmic losses. We conclude that the most appropriate design can be found from multi-criteria optimization, resulting in a Pareto-frontier on the dependencies of TEP vs TV computed for all studied geometries. The proposed approach helps us to determine a restricted number of geometries for more detailed 3D computations and further experimental validations on prototypes.

Reindeer (Rangifer tarandus) have evolved elaborate nasal turbinate structures that are perfused via a complex vascular network. These are subject to thermoregulatory control, shifting between heat conservation and dissipation, according to the animal’s needs. The three-dimensional design of the turbinate structures is essential in the sense that they determine the efficiency with which heat and water are transferred between the structure and the respired air. The turbinates have already a relatively large surface area at birth, but the structures have yet not reached the complexity of the mature animal. The aim of this study was to elucidate the structure–function relationship of the heat exchange process. We have used morphometric and physiological data from newborn reindeer calves to construct a thermodynamic model for respiratory heat and water exchange and present novel results for the simulated respiratory energy losses of calves in the cold. While the mature reindeer effectively conserves heat and water through nasal counter-current heat exchange, the nose of the calf has not yet attained a similar efficiency. We speculate that this is probably related to structure-size limitations and more favourable climate conditions during early life. The fully developed structure–function relationship may serve as inspiration for engineering design. Simulations of different extents of mucosal vascularization suggest that the abundance and pattern of perfusion of veins in the reindeer nasal mucosa may contribute to the control of temperature profiles, such that nasal cavity tissue is sufficiently warm, but not excessively so, keeping heat dissipation within limits.