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Multi-walled carbon nanotubes (MWCNTs) were grown by plasma-enhanced chemical vapor deposition (PECVD) in a bell jar reactor. A mixture of methane and hydrogen (CH4/H2) was decomposed over Ni catalyst previously deposited on Si-wafer by thermionic vacuum arc (TVA) technology. The growth parameters were optimized to obtain dense arrays of nanotubes and were found to be: hydrogen flow rate of 90 sccm; methane flow rate of 10 sccm; oxygen flow rate of 1 sccm; substrate temperature of 1123 K; total pressure of 10 mbar and microwave power of 342 Watt. Results are summarized and significant main factors and their interactions were identified. In addition a computational study of nanotubes growth rate was conducted using a gas phase reaction mechanism and surface nanotube formation model. Simulations were performed to determine the gas phase fields for temperature and species concentration as well as the surface-species coverage and carbon nanotubes growth rate. A kinetic mechanism which consists of 13 gas species, 43 gas reactions and 17 surface reactions has been used in the commercial computational fluid dynamics (CFD) software ANSYS Fluent. A comparison of simulated and experimental growth rate is presented in this paper. Simulation results agreed favorably with experimental data.