Abstract
Many natural systems that transport heat, energy or fluid from a distributed volume to a single flow channel exhibit an analogous appearance to trees (examples include bronchial tubes, watersheds, lightening, and blood vessels). Several authors have proceeded with analytical methods to develop fractal or pseudo-fractal designs analogous to these natural instances. This implicates an implicit belief in some designers that there is an optimal attribute to this 'tree-like' appearance. A novel explanation for the appearance of these systems is presented in this paper. Natural systems follow the path of least resistance; or in other words, minimize transport effort. Effort is required to overcome all forms of friction (an unavoidable consequence of motion). Therefore effort minimization is analogous to transport distance (path length) minimization. Effort due to friction will be integrated over the total transport distance. Leveraging this observation a simple, geometric explanation for the emergent 'tree-like' architecture of many natural systems is now achievable. Note that this 'tree' effect occurs when most of the flow volume exhibits diffusion, with a small percentage of interdigitated high flow velocity channels. One notable application of our novel method, path length analysis, is the automated creation of cooling channel networks for heat generating micro-chips. As a demonstration, this path length analysis method was used to develop a significantly more efficient channel configuration (by 14%) than the state of the art for conductive microchip cooling. An extensive array of finite element models confirms the performance of this novel configuration.