1 Copyright © 2012 by ASME Proceedings of the 14 th International Design Engineering Technical Conference DAC38 August 12-15, 2012, Chicago, Illinois, USA DETC2012-71448 NOVEL TOPOLOGICAL APPROACH TO DESIGNING FLOW CHANNELS Bradley Camburn Camburn@utexas.edu Kristin Wood Wood@mail.utexas.edu The University of Texas at Austin Austin, Texas, USA Richard Crawford RHC@mail.utexas.edu 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. Commonly for natural and designed systems with this type of flow, the flow volume consists primarily of high resistance regimes with a smaller portion of interdigitated low resistance regions (flow channels). Perhaps, the most relevant design problem is cooling of a microchip. Since microchip performance is optimal at lower temperatures, bulk heat flow resistance for heat exiting the system should be minimized; therefore, it is critical to cleverly align the channel to maximize flow. Heat conduction from a microchip is typically simplified into heat conduction from a homogenously heat-generating plate. This simplified problem is used as a standard model with which engineering designers can compare the performance of various cooling configurations. Due to the apparent tree-fractal characteristics of empirically emerging systems (i.e. in nature), several authors have examined analogous, simplified fractal configurations. These fractal configurations appear to be the best solution in current publication. We present a novel topological analysis that provides insight into performance at a schematic level. This analysis leads to the development of a new configuration, leaf- like, which outperforms the current state-of-the-art. Performance is compared among the configurations with two parallels analyses: an extensive series of finite element models, covering a broad combinatory array of material properties and heating conditions; and topological analysis of path length, or the average distance heat, energy or fluid, must travel through the substrate and channel media before exiting through the point flow channel. There is a strong correlative mapping between the two analyses. Finite element modeling is employed because it provides a fundamental mechanics approach to assessment of heat transfer behavior, while the path length analysis provides an intuitive and computationally affordable means to predict performance. Novel contributions of this work include a configuration for conductive cooling in a plate for VTP flow, superior to the state-of-the-art, and a topological analysis of VTP flow that provides a generalized metric of bulk flow resistance and a schematic level conceptualization of the mechanics of VTP flow. Future advancements of our research could include enhancing the algorithm to automatically parse geometry into channel segments from an image or other external representation and eventually to even generate a suitable channel from arbitrary substrate geometry. INTRODUCTION A common feature among arteries, lightening, bronchial airways, leaves, and watersheds is truncated tree-like fractal organization. This commonality may be due to the fact that these systems solve a similar type of problem- the transference of energy or matter from a distributed arrangement (area or volume) to a single point (sink) [1]. The motivation of this paper is to examine whether the tree-like fractal found so frequently in nature is in fact optimal for volume-to-point flow. For the volume-to-point flow problem the amount of flow channel is constrained. Therefore, it is important to optimally arrange the available channel. The approach of this paper is an in-depth look at theoretical analysis and experiments about one type of volume-to-point flow. This paper will focus on evaluating the problem of conduction from a heat generating plate to a sink point- analogous to cooling a microchip. In the past, tree like fractal channel geometry has been proposed for this type of cooling [4]. In order to evaluate this proposal, the performance of various geometries is compared via literature review and analyses. NOMENCLATURE Fractal, conduction, path length, finite element, volume to point flow, topology.