A constructal view of prefractal dendritic flow networks using an exergy analysis

Abstract

Evidence supports the interpretation that natural dendritic networks are described by fractal theory. It is recognised that the fractal description alone is not a complete description of nature of space filling. This study addresses the fundamental question of what the size of dendritic flow networks should be, in order to perform with the least irreversibilities, in addition to what fractal features-based pattern should have. Optimal shapes of symmetric and asymmetric networks for viscous flow and diffusion with junction loss effects are analysed based on exergy minimisation rate. Global size constraints included in the analysis are the volume and surface area. The optimal sizes of the flow networks are obtained, and prefractal dimensions that characterise these networks are computed. It is shown that the prefractal dimensions depend on both fluid transport mechanisms and space constraints. The physics link between prefractal regularity and optimal flow performance is clear presented.