Flows through porous media have been studied extensively during the past two decades. This lecture reviews an emerging body of work centered on the idea that the porous structure (spacings, arrangements) can be optimized such that the global flow system achieves the highest performance under size constraints. The simplest demonstration of this 'constructal' principle is the existence of an optimal spacing between parallel plates, in a large stack of many fine spacings, when the global objective of the stack is to transfer heat or mass with minimal resistance. Stacks with optimized parallel-plates spacings are common in nature and engineering design, from fish gills to heat exchanger fins and turbine blades and vanes. The performance of such flow structures can be improved by inserting smaller plates in the mouths of the previously optimized parallel-plates channels. Performance is further improved if even smaller plates are placed in the narrower mouths formed by the first generation of plate inserts. This design sequence can be continued, however, diminishing returns are reached. The result is a nonuniform multi-scale flow structure that packs the highest transport density. The analogy between this unidirectional multi-scale flow structure (parallel plates) and natural two- and three-dimensional multi-scale structures (e.g., trees) is discussed.
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