Heat transfer in flow through branching tubes

Allometric scaling relations for how branching tubes deliver fluid are often based on the assumption of isothermal conditions which are not always fulfilled. This work reports on the sizes of branching tubes for fluid flow subjected to constant wall heat flux. It explores how the delivery of fluid and heat influences the optimal size of a tube and the optimal configuration of branching tubes for both laminar and turbulent flow. Besides, it presents an analytical basis for evaluation of optimal size of tubes that minimise the power loss associated with the pumping power and the heat transfer. The findings obtained in this study may have important implications for design of systems with minimum thermodynamic losses.