Carbon nanotubes (CNTs) possess exceptional mechanical, electrical and thermal properties by virtue of their unique physical structures. In recent decades, continued efforts have been made to develop techniques for producing CNTs on an industrial scale. The floating catalyst chemical vapour deposition (FCCVD) method has been widely accepted as a promising technique for mass production of CNTs. Despite the recent progress in improving the technique, a lack of fundamental understanding of the limiting factors and the underlying mechanisms of CNT synthesis makes it difficult to scale up the production to meet the ever-growing industrial demands. The present study aims to develop numerical and experimental approaches to extend our understanding of CNT synthesis, and ultimately help develop methods for mass production of CNTs. A multi-phase thermodynamic equilibrium model consisting of C, H, O, Fe and S elements, at stoichiometries and temperatures consistent with CNT synthesis using the FCCVD method was developed. The effects of variable amounts of the different elements, as well as inert species (Ar and N₂) on the species and phase distributions were investigated as a function of temperature at atmospheric pressure. The results reveal that the threshold formation temperature for graphitic carbon products, C(s), increases with the H/C molar ratio. The addition of sulphur into synthesis suppresses the formation of α-Fe(s) in favour of FeS(s). Solid iron carbide Fe₃C(s) takes up all Fe atoms beyond 700 °C, which then turns into liquid phase or dissociates into vapourised Fe(g) beyond 1250 °C. The effect of the estimated bulk Gibbs free energies for different types of CNTs in lieu of C(s) show little change to the overall species and phase distributions within the estimated uncertainties. The effect of inert gases Ar and N₂ relative to H₂ as a carrier gas is found to be a lowered threshold formation temperature for C(s), from ~700 °C in H₂ down to ~100 °C. The formation of C(s) is significantly affected O/C molar ratios where no C(s) shall be formed at O/C > 1.0. Carbon nanotubes were produced using a premixed laminar flat flame burner where a H₂/air flame was used to provide heat, while feedstocks containing various proportions of carbon and catalyst precursors (ethanol, ferrocene and thiophene) were injected through a central tube to the post flame region. The as-produced nanomaterials were collected at downstream of the post-flame region at a height above burner of 230 mm. Various techniques were used to characterise the collected samples including Raman spectroscopy, energy-dispersive X-ray spectroscopy (EDX), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). A formation window in the equivalence ratio range φ=1.05-1.20 was identified, and the flame temperature was found to be the dominant limiting factor for the inception of CNTs. CNTs bundles were formed and the diameter of individual CNTs were observed to be lower than 5 nm. The formation of CNTs was accompanied by a production of highly crystalline nanoparticles of a size between 20 nm and 100 nm. These nanoparticles were identified as iron oxides and/or elemental iron nanoparticles by EDX. We studied the role of thiophene in flame synthesis of CNTs for the first time, and found the number density and the overall length of CNTs were markedly improved by adding thiophene to the precursor mixture. The optimum range of the mass ratios of sulphur to iron elements in the catalyst precursors was determined to be 0.1-2.0. A 2-D diffusion model was developed to assist the understanding of the flame method. The spatial distributions of mixture fraction, local temperature, and axial velocity of flows were obtained. This model serves as a pivotal that links all the numerical methods developed in the thesis, and has the capability of estimating a spatially-resolved species distribution for the flame synthesis. The present project both numerically and experimentally studied CNT synthesis, and extended our understanding of the fundamental mechanisms, shedding light into possible routes for mass production of CNTs.