Multi-dimensional effect on optimal network structure for fluid distribution

Optimization of a fluid distributing tube network plays a critical role in the operation efficiency and energy conservation of a cooling system. In this paper, we analyze the effect of multi-dimension on the structure of a fluid distributing tube network for cooling heat-generating, and then seek the optimal fluid structure with minimal pressure drop for a given total volume of the tube network. The theoretical results show that the pressure drop of a laminar flow in the tube network reaches the minimum when the cubic value of the parent tube diameter equals to the sum of those of the daughter tube diameter, consistent with Murray's law. Furthermore, it is advantageous to have a higher dimension structure in network arrangement when the number of heat generation units increases, i.e., network performance improves by adopting a two-dimensional and even three-dimensional format as the number of units grows.