Scale Analysis for Optimal Pattern Formation in Flow Systems

The occurrence of flow pattern can be predicted based on constructal law. Scale analysis is a method for deriving the essential information based on the basic principles of fluid flow and heat transfer. It provides order-of-magnitudes but also the form of the functions that describe the quantities understudy. In flow systems, patterns (configuration, design, architecture) arise from competition between competing trends, at least two modes of transport or locomotion: slow (diffusion, walk, etc.) and fast (streams, run, etc.). Optimal patterns mean the best flow access and the best balance between these trends. The study presented here follows from the scale analysis together with constructal and, is illustrated by examples from simple water heating to human locomotion.