A computational methodology for optimization of fin shapes is formulated and demonstrated in the context of steady, laminar, fully-developed forced convection in a straight duct of circular cross-section, with air as the fluid and non-twisted, uninterrupted, longitudinal internal fins made of steel, aluminium, and copper. The governing equations are solved using finite volume methods. The fins shapes are approximated using non-uniform rational B-splines. with the control points as design variables. A gradient-based method is used for the optimization. Results pertaining to the maximization of suitably defined thermal performance, subject to constant pumping power per unit length, are presented and discussed. (C) 2009 Elsevier Ltd. All rights reserved.