Molecular dynamics based heat-flux auto-correlation functions are combined with a Green-Kubo relation from the linear response theory to quantify the lattice contribution to thermal conductivity of single-walled carbon nanotubes with three different chiralities (screw symmetries). The interactions between carbon atoms within a nanotube are analyzed using the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. The results obtained show that, due to a long-term exponential-decay character of the heat-flux auto-correlation functions, converging values of the lattice thermal conductivities can be obtained using computational cells considerably smaller than the phonon mean free path. However, to obtain accurate values of the thermal conductivity, a spectral Green-Kubo relation and a phonon-based extrapolation function are found to be instrumental for quantifying the thermal conductivity contribution of the long-wavelength phonons not allowed in the computational cells of a finite size. The results further show that chirality of the carbon nanotubes can affect the lattice contribution to the thermal conductivity by as much as 20%. Also, the simulation results of the effect of temperature on the thermal conductivity clearly show a competition between an increase in the number of phonons and an increased probability for phonon scattering at higher temperatures. (C) 2005 Springer Science + Business Media, Inc.