The thermal performance of vertically oriented, internally finned tubes in natural convection is optimized analytically. The total heat transfer rate is selected as the objective function for the optimization under a constraint of given base-to-ambient temperature differences. In order to predict the total heat transfer rate, a new correlation of the heat transfer coefficient is developed using the asymptotic method. In order to validate the new correlation, experiments are performed for internally finned tubes with different geometries. With the new correlation, the three parameters of fin geometry, i.e. fin thickness (t), fin height (H), and number of fins (n(fin)), are optimized under given tube sizes of tube diameter (D) and tube length (L). Finally, closed-form equations for the optimal fin geometry are proposed as design guidelines for internally finned tubes with various sizes: t(opt) = 5.44 x 10(-3)D, H-opt = 0.388D, and n(fin,opt) = 0.588(D/L)(PrRaL1/4)-Ra-1/4. (C) 2015 Elsevier Ltd. All rights reserved.