The objective of this paper is to determine the thermal conductivity of Zinc Oxide nanowire by Steady State Non-equilibrium and Transient Non-equilibrium Molecular Dynamics (SS-NEMD and T-NEMD) simulations using the ReaxFF reactive force field . While SS-NEMD uses an equilibrated system and statistical averaging; T-NEMD uses cooling/heating rates in order to calculate the conductivity. The validity of the methods is first verified using Argon as a test case. The thermal conductivity of Argon thus calculated is compared with those presented by Bhowmick and Shenoy . We then study the effects of system size using SS-NEMD method while effects of periodic boundary conditions - 1D, 2D and bulk variation of conductivity with temperature are analyzed using T-NEMD simulations. The results obtained compare favorably with those measured experimentally [12, 13]. Thus the SS-NEMD and T-NEMD methods are alternatives to the traditional Green-Kubo approach. In conjunction with ReaxFF, they are computationally cheaper than the Green-Kubo method and can be used to determine the thermal conductivity of materials involved in surface chemistry reactions such as catalysis and sintering.