  We investigate the thermal conductivity in the armchair and zigzag MoS$_{2}$
nanoribbons, by combining the non-equilibrium Green's function approach and the
first-principles method. A strong orientation dependence is observed in the
thermal conductivity. Particularly, the thermal conductivity for the armchair
MoS$_{2}$ nanoribbon is about 673.6 Wm$^{-1}$K$^{-1}$ in the armchair
nanoribbon, and 841.1 Wm$^{-1}$K$^{-1}$ in the zigzag nanoribbon at room
temperature. By calculating the Caroli transmission, we disclose the underlying
mechanism for this strong orientation dependence to be the fewer phonon
transport channels in the armchair MoS$_{2}$ nanoribbon in the frequency range
of [150, 200] {cm$^{-1}$}. Through the scaling of the phonon dispersion, we
further illustrate that the thermal conductivity calculated for the MoS$_{2}$
nanoribbon is esentially in consistent with the superior thermal conductivity
found for graphene.
