This paper examines the degree of irreversibility, or thermodynamic nonideality, in a tree-shaped flow network with a constant wall heat flux. The tree network is a dichotomic and homothetic structure, and a fully developed laminar flow of Newtonian and non-Newtonian power law fluids is assumed. We investigate (i) the characteristics of the tubes composing the network (i.e., variation in the homothetic ratios of length and diameters, as well as variation in wall permeability of tubes), (ii) the existence of blocked (obstructed) tubes in the network, (iii) fluid characteristics, and (iv) frictional and thermal effects on entropy generation. The influence of parameters like the fluid behavior index, Reynolds number, Nusselt number, homothety ratios for length and diameters, and wall permeability is hence evaluated. Finally, the degree of thermodynamic irreversibility associated to tree networks designed for a maximum flow access is determined. (C) 2015 Elsevier Ltd. All rights reserved.