Based on non-equilibrium molecular dynamics, a model is developed to study the thermal conductivity of Single Wall Carbon Nanotube (SWCNT) inside filled with Copper (Cu), forming a coaxial composite in the form of a nanowire. The Nose-Hoover thermostat is used to maintain the opposing ends of the SWCNT-Cu nanowire at uniform temperatures of 320 K and 280 K. Firstly, the length dependent thermal conductivities are examined in vacuum using the simulated axial temperature profiles and by applying the Nose-Hoover thermostat. The effective thermal conductivity of copper nanowire is estimated based on the electrical resistance analogy. The calculations showed that the thermal conductivity of a SWCNT-Cu nanowire is up to 24% higher than that of a corresponding pure SWCNT. Secondly, the identical SWCNT-Cu nanowire is placed in water instead of vacuum. The conduction along the radial direction of this coaxial nanocomposite surrounded with water is examined. Due to its simplicity and adaptability, a simple point-charge water model is implemented. Using the Nose-Hoover thermostat, the copper core is kept at a uniform temperature as a heat source, and a circular edge layer of water is kept at a lower temperature as a heat sink in order to impose a radial temperature distribution. The temperature jump due to interface resistance at the SWCNT-water interface is found to be smaller than the temperature jump at the SWCNT-Cu interface.