optimal tree-shaped networks for fluid flow in a disc-shaped body

摘要

In this paper we consider the fundamental problem of how to design a flow path with minimum overall resistance between one point (O) and many points situated equidistantly on a circle centered at O. The flow may proceed in either direction, from the enter to the perimeter, or from the perimeter to the center. This problem is an integral component of the electronics cooling problem of how to bathe and cool with a single stream of coolant a disc-shaped area or volume that generates heat at every point. The smallest length scale of the flow structure is fixed (d), and represents the distance between two flow ports on the circular perimeter.