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The Kapitza resistance (Rk) at the water-carbon nanotube (CNT) interface, with water on the inside of the nanotube, was investigated using molecular dynamics simulations. We propose a new equilibrium molecular dynamics (EMD) method, also valid in the weak flow regime, to determine the Kapitza resistance in a cylindrical nanoconfinement system where nonequilibrium molecular dynamics (NEMD) methods are not suitable. The proposed method is independent of the correlation time compared to Green-Kubo-based methods, which only work in short c