Abstract Plasma assisted CO₂ dissociation has recently been the topic of many studies. The production of chemical fuels from environmentally unfriendly CO₂ through supersonic nozzles is one of the most prominent approaches under investigation. However, the experiments show that the theoretical conversion rates are far away from being achieved. In this study, two-dimensional fully coupled cases are investigated. This brings insights about how the CO₂ dissociation can be improved; mainly by a correct design of nozzles. The proper shape of a nozzle is a fundamental aspect to be taken into account numerically and in experiments to avoid undesirable phenomena such as the occurrence of shocks. The proper design of the nozzle shape leads to a shock-free flow being uniform at the nozzle outlet. A high degree of cooling can be achieved in a shock-free nozzle. Moreover it is shown that there is no optimal value for Mach number provided that the nozzles are sized properly. If the sizing is done correctly, it is found that higher Mach numbers lead to higher degree of non-equilibrium and thereby to higher dissociation rate. The sizing of the nozzle to maximize the departure from equilibrium in the nozzle is the final key of an efficient CO₂ dissociation. Finally, the results are compared with those of a semi-analytical method to conclude that if the nozzle is conceived in a proper way, simpler approaches can also give satisfactory results.