Fractal-Like Flow-Fields with Minimum Entropy Production for Polymer Electrolyte Membrane Fuel Cells.

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 (Dh), cross-sectional area (DΣ) and hydraulic resistance (DZ). 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 Dh -, DΣ -, and DZ -based tubes (Cases 1-3). Appropriate scaling of the fractal system providing uniform entropy production along all the channels have also been computed for Dh -, DΣ -, and DZ -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 DΣ -based models gave smaller resistances compared to the original rectangular channels and, therefore, underestimated the TEP. The DZ -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.

Energy efficiency of respiration in mature and newborn reindeer.

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.

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.

Biomechanical analysis of asymmetric mesio-distal molar positions loaded by a symmetric cervical headgear.

PURPOSE: The plane 2D model and 3d finite element model of the headgear attached to two molars with different mesio-distal location are studied to show the asymmetric mechanical effects produced by symmetrically loaded headgear. In daily dental practice the asymmetrical location of molars is usually ignored. METHODS: Six 3D finite element models of a symmetric cervical headgear were designed in SolidWorks 2011. The models showed symmetric molar position (model 1), 0.5 to 2 mm of anterior-posterior molar difference (models 2-5) and a significant asymmetry with 10 mm of difference in the locations (model 6). The head gear was loaded with 3N of force applied at the cervical headgear. The forces and moments produced on terminal molars are assessed. RESULTS: It is shown the difference between the forces acting at the longer and shorter outer arms of the headgear increases with increase in the distance. The significant numeric difference in the forces has been found: from 0.0082 N (model 1) to 0.0324 N (model 5) and 0.146 N (model 6). These small forces may produce unplanned distal tipping and rotation of the molars around their vertical axes. The most important funding was found as a clockwise yaw moment in the system when is viewed superio-inferiorly. The yaw moment has been computed between -0.646 Nmm (model 1) and -1.945 N mm (model 5). CONCLUSIONS: Therefore even small asymmetry in location of molars loaded by a symmetric cervical headgear will produce undesirable movement and rotation of the teeth that must be taken into account before applying the treatment.

Finite element method (FEM) analysis of the force systems produced by asymmetric inner headgear bows.

BACKGROUND: Extra-oral traction appliances were introduced more than a century ago and continue to be used to produce orthopaedic and/or dental changes in the maxilla. While force systems produced by asymmetric outer bows have been studied extensively, the force systems produced by asymmetric inner bows have been overlooked. AIM: To analyse the forces acting on the maxillary first molars: when the size of one bayonet bend is increased; when the point of application of the distalising force on the inner bow is moved to one side; when one molar is displaced palatally. METHODS: Four FEM models of cervical headgear attached to maxillary first molars were designed in SolidWorks 2010 and transferred to an ANSYS Workbench Ver. 12.1. Model 1, each molar was 23 mm from the midpalatal line and the inner bow was symmetrical; Model 2, the left molar was displaced 4 mm towards the midpalatal line and the inner bow was symmetrical; Model 3, the molars were equidistant (23 mm) from the midpalatal line, but the left molar was engaged by a 2 mm larger bayonet bend; Model 4, the molars were equidistant (23 mm) from the midpalatal line but the join between the inner and outer bows was displaced 2 mm towards the left molar. In all FEM models, a 2N force was applied to the inner bow at the join between inner and outer bows and the energy transmitted to the teeth and the von Mises stresses on the molar PDLs were assessed. RESULTS: There were marked differences in the strain energy on the teeth and the von Mises stresses on their PDLs. A 14 to 20 per cent increase in energy and force was produced on the tooth closer to the symmetric plane of the headgear. In addition, the increase in energy produced a 30 to 62 per cent increase in the von Mises stresses within the PDLs. CONCLUSION: Small asymmetries in molar position, the size of a bayonet bend and the point of application of a force on an inner bow resulted in asymmetrical forces on the molars. These forces were higher on the molar closer to the symmetric plane of the headgear.