In the present work the effect of viscous dissipation on the heat transfer in a finned tube cooled by a fluid in laminar flow is studied under the condition of imposed heat flux. In particular, the alterations induced by viscous dissipation in the optimum finned tube geometries are investigated. To this aim, the velocity and temperature distributions on the finned tube cross-section are determined with the help of a finite element model which takes the effect of viscous dissipation into account. Moreover, a global heat transfer coefficient is calculated. After having assigned a polynomial lateral profile to the fins of the tube, the geometry is then optimized in order to maximize the heat transferred per unit of tube length for a given weight and for a given hydraulic resistance in correspondence with different intensities of viscous dissipation. Lastly, the differences between the optimum geometries obtained under different conditions of viscous dissipation are analyzed. (C) 2004 Elsevier Ltd. All rights reserved.