The present work theoretically and numerically reexamines the Murray's law to design a tree-like rectangular microchannel network with constant microchannel height under the constraint of constant total channel volume, and investigates effects of the dimensional and structural parameters of the tree-like network on the optimal width ratio and optimal hydraulic diameter ratio of rectangular microchannels at two successive branching levels to achieve a minimum hydraulic resistance. The results show that the optimal hydraulic diameter ratio of the tree-like rectangular microchannel network does not follow the conventional Murray's law. Both the optimal width ratio and the optimal hydraulic diameter ratio to achieve a minimum hydraulic resistance strongly depend on the dimensional and structural parameters including rectangular channel height H, total channel volume V, channel length ratio gamma, channel length at the initial branching level L-0, branching number N and branching level m of the tree-like network. Additionally, the present work finds that the average convective heat transfer coefficient of a heat sink with an elementary T-shaped tree-like rectangular liquid-cooling microchannel network with the constant channel height increases with both the increasing width ratio of microchannels at two successive branching levels and the increasing channel height. (C) 2018 Elsevier Ltd. All rights reserved.