In the present work the geometry of annular ducts with asymmetrical longitudinal fins is optimized in order to enhance the heat transfer under laminar coolant flow conditions. The heat transferred is also ma;maximized for a given amount of material material or hydraulic resistance, Polynomial profiles are assigned to the two lateral fin surfaces. Velocity and temperature distributions on the annular duct cross section are determined with the help of a finite-element model. A global heat transfer coefficient and an equivalent Nusselt number ape then calculated. Lastly, optimum asymmetrical fins obtained by means of a genetic algorithm are shown for different situations and their performance is compared with those of optimum symmetrical fins.