Tree-Shaped Flow Structures Viewed from the Constructal Theory Perspective

The generation of flow configuration (design, shape, structure, patterns, rhythms) is a phenomenon that occurs across the board, in animate and inanimate flow systems. Scientists have struggled to understand the origins of this phenomenon. Among the configurations, tree-shaped structures dominate the design of natural and man-made flow systems. Why are they so important? Is there a physics principle from which their configuration can be deduced?

Constructal theory, conceived by Adrian Bejan, is the view that the generation of configuration in nature is a universal phenomenon, which is covered by a law of physics-the constructal law. This chapter addresses the generation of tree-shaped design in the light of constructal theory. First, we briefly review the constructal theory that is applicable to animate and inanimate flow systems. Next, we review the studies that are focused on the constructal view of tree-shaped flow structures. The constructal theory presented in this chapter introduces a new paradigm that is universally applicable in nature, engineering and social sciences.

Keywords: Constructal theory, design in nature, topology optimization, lungs, tree networks, dendritic, flow geometry, constructal design, Murray law, tributaries streams, rivers basins, oscillatory flow.