Constructal design for X-shaped hot water network over a rectangular area

An X-shaped hot water network model with thermal insulation layers is built. Constructal optimizations of elemental, first order and the higher order assemblies of the network are performed by taking minimum overall pressure drop and maximum overall temperature difference as optimization objectives. The results show that for any higher order assembly of the network, optimal internal radius ratio is always 21/2 for wetted surface constraint, and 23/7 for total duct volume constraint. The optimal radius ratio relationship is Rj−1lnRj−1/(RjlnRj) = ri,j/ri,j−1 (j = 1,2,3,…,n) for the two constraints, where ri and R are the internal radius and the radius ratio of the insulation material, respectively. Compared the overall temperature difference performance of the X-shaped hot water network with that of the H-shaped network, the overall temperature difference of the X-shaped network is increased by 67.53%, and the overall pressure drop is decreased by 13.86% when heat loss unit number is 0.1. Therefore, the performance of the hot water network can be evidently improved by adopting the model with X-shaped structure.