Considering the three-phonon process, we calculate the thermal conductivity of zigzag tubes. It is found that thermal conductivity of an isolated ͑6, 0͒ single-walled carbon nanotube increases with the increase of temperature at low temperature, and would show a peak behavior at about 85 K before falling off at high temperature. Moreover, thermal conductivity is high for single-walled carbon nanotubes with small diameters as compared to the tubes with large diameters. The thermal conductivity at 300 K is approximately inversely proportional to the tube's diameter.Potential applications of carbon-nanotube-based devices, such as diodes, 1 field-effect transistors, 2 single-electron transistors, 3 as well as elementary logic circuits 4 rely on an effective way of removing high density of excess heat from the device active regime. 5-7 Removal of heat, actually, depends on the thermal conductivity of carbon nanotubes and the related compounds. 8 Thermal conductivity of singlewalled carbon nanotubes ͑SWCN's͒ is predicted to be unusually high by molecular-dynamics simulations at room temperature. 9-11 The measurement on ropes of SWCN's indicates a linear temperature dependence up to 30 K and an upward bend near 30 K on the curve of thermal conductivity (T). 12 In contrast to that of SWCN's, for multiwall carbon nanotube ͑MWNT͒ ropes increases with temperature in a parabolic fashion at low temperature up to ϳ120 K. 13 In order to reveal temperature dependence behavior of , Kim 14 performed scanning electron microscopy technique on individual MWNT. It is found that at low temperature (8 KϽT Ͻ50 K), increases following a power law with an exponent 2.50, and then increases quadratically when T Ͻ150 K. Although there is a vast literature concerning thermal transport in SWCN's, it is necessary to describe phonon characteristics for understanding the physical essence of the various experimental observations. In this paper, considering the three-phonon umklapp process, we analyze the physical mechanics of the thermal transport in a perfect isolated SWCN.As heat in SWCN's is mostly carried by acoustic phonons, it is reasonable to neglect the electronic component of thermal conductivity. The expression for lattice thermal conductivity at a given temperature T can be written as 15,16where , C , and V are phonon relaxation time, specific heat, and phonon group velocity of phonon mode , respectively. In a perfect isolated SWCN, phonon relaxation time is mainly controlled by boundary scattering and three-phonon umklapp scattering process. So, the total phonon relaxation time is usually given by the Matthiessen rule as 17with the relaxation-time parameters for boundary scattering B and for three-phonon umklapp scattering process U . Here, we choose B ϭ50 ps to be independent of temperature and phonon energy. 12,14,[19][20][21] From the first-order perturbation theory, the relaxation time U in the three-phonon umklapp process for thermal modes q is given by 18where ␥ is the Gruneisen parameter, ប is the Planck constant, M is atomic mas...