In this paper, we optimize the performance of several classes of simple flow systems consisting of T- and Y-shaped assemblies of ducts, channels and streams. In each case, the objective is to identify the geometric configuration that maximizes performance subject to several global constraints. Maximum thermodynamic performance is achieved by minimization of the entropy generated in the assemblies. The boundary condition is fixed temperature of the channel wall. The flow is assumed laminar and fully developed. Every geometrical detail of the optimized structure is deduced from the constructal law. Performance evaluation criterion is proposed for evaluation and comparison of the effectiveness of different tree-shaped design heat exchangers. This criterion takes into account and compare the entropy generated in the system with heat transfer performance achieved. (c) 2006 Elsevier Ltd. All rights reserved.