Constructal theory uses a tree network of conducting paths to discharge the heat generated in a uniform heat generating area to a heat sink located on its border. Constructal theory aims to decrease the global thermal resistance, in other words, to improve the heat flow performance of the heat generating area by increasing the complexity of the tree network of conducting paths. In this work, a second law analysis is applied to the optimal uniform heat generating areas with different complexity levels of the tree network of conducting paths. Comparing the entropy generation numbers (EGN) derived for the heat generating areas with different internal complexities shows that the heat flow performance does not essentially improve if the internal complexity of the heat generating area increases. (C) 2004 Elsevier Ltd. All rights reserved.