Entropy generation in fully-developed flow through a duct with heat transfer is discussed. Methods are presented to minimize entropy generation by adjusting the shape of the duct's cross-section. Choosing a different cross-sectional shape allows for control of the competing fluid flow and heat transfer irreversibilities. By controlling the competing irreversibilities, the total entropy generation rate can be minimized. Given the flow rate, heat transfer rate, available cross-sectional area, and the fluid properties, a general design correlation is presented that allows for a determination of the optimal shape of a duct. (C) 2009 Elsevier Ltd. All rights reserved.