A hybrid numerical technique which combines the differential transformation and finite difference method is utilized to investigate the annular fin with temperature-dependent thermal conductivity. The exposed surfaces of the fin dissipate heat to the surroundings by convection and radiation. The influences of the convective heat transfer coefficient, absorptivity, emissivity and thermal conductivity parameter on the temperature distribution are examined. The results show that the convective heat transfer plays a dominant role for heat dissipation under the convection-radiation condition. The optimum radii ratio of fin which maximizes the heat transfer rate and fin efficiency is also discussed. (C) 2011 Elsevier Ltd. All rights reserved.