Optimization of a Fractal Treelike Microchannel Network with Uniform Roughness for Laminar Flow

Considering the excellent transport performance of treelike networks and the effect of roughness on fluid flow in a microchannel, the present work studied the optimization of a symmetric treelike roughened network with minimum hydraulic resistance under constant total channel base volume. It was found that there is an optimal base diameter ratio beta(m) of channels at two successive branching levels that minimizes the hydraulic resistance of the network. The beta(m) value increases with increasing average roughness height. A larger beta(m) value is needed to minimize the hydraulic resistance of the network with larger branching number N, branching level m, and channel length ratio gamma, because the increases in N, m, and gamma reduce the channel diameter and magnify the influence of roughness on the fluid flow.