Fluid flow in a porous tree-shaped network: Optimal design and extension of Hess–Murray’s law

This paper aims to contribute to the ongoing research on tree-shaped flow structures. Here, we focuses on porous-walled tree-shaped networks, namely the laminar fluid flow. Analytical models are developed for pressure distribution along the porous tree-network and for the hydraulic resistance of the network in terms of geometry of successive vessel segments, number of branches, branching levels and intrinsic permeability of walls. We also rely on constructal design to find important insights regarding the allometric relationships between the sizes of successive vessel segments of tree networks.