The emergence of the constructal element in tree-shaped flow organization

This paper presents how the elemental systems of constructal tree-shaped flows originate (Bejan, 2000) [1]. It is at the elemental system level where the transport (flow) turns from slow (volumetrically) to fast (aligned) thus making the essential connection between an infinity number of points to a finite entity. That is the only mathematically and physical way one can make such connection. The elemental system is the smallest scale of volume-to-point flows that occur in Nature (e.g., lungs, river deltas, botanical trees and their roots, canopies and leaves veins) and Engineering (e.g., photovoltaic metallic contacts networks). They are explained and predicted by Constructal Theory (CT). In this paper the elemental system starts its design evolution in a simpler configuration to reach the configuration that is otherwise assumed in Constructal Theory and fractals publications alike. The design evolution takes place in a combination of evolutionary computing, Constructal Law and finite element analysis. An original computer code performs the algorithm. Results showed that (a) the constructal element evolves to a configuration very similar to ones customarily assumed in CT, but with the high-conductivity insert shorter, leaving a gap at the far end; (b) the resulting configurations are nearly path independent; and (c) the gain in performance resembles an S curve, and it is explained theoretically.