## 1 Introduction  
Hydrogen production and energy release during its combustion are some of the most promising solutions for a sustainable future in the energy sector. For NO\({}_{x}\) reduction and to avoid safety risks related to the high hydrogen-air flame speed (up to 50 m/s) and low quenching diameters (up to 0.5 mm), required to ensure prevention of the flashback in case of the fully premixed burner concepts, several micro-mixers or micro-nozzle burner solutions were recently patented and results of their operation reported in the literature [1; 2; 3]. To optimize the flame stability and combustion properties of H\({}_{2}\), a common approach is the modification of the burner or nozzle geometry [4; 5; 6]. In this regard, previous studies deal with the comparison of different combustion models using detailed chemistry and concluded that the reduced reaction mechanism method showed the best agreement with experiments in terms of capturing and mapping the typical flame structure [3; 7]. Moreover, several studies indicated that the consideration of component-specific diffusion has a non-negligible impact on the component distribution during the combustion and the propagation characteristics of the flame [8; 9; 10; 11]. Further numerical investigations of the ignitability of hydrogen and the analysis of the combustion process have been done by [PERSON] et al. [12] and [PERSON] et al. [13]. Whether the group of [PERSON] et al. focused on the numerical perspective and the critical conditions during the ignition process, [PERSON] et el. analyzed the combustion characteristics and obtain critical parameters and determine an optimal operation modus also experimentell. Focusing on the flammability limit of hydrogen [PERSON] et al. were able to determine the risk of a hydrogen flame by developing and validating a model for various hydrogen-air mixtures [14]. The importance of considering differential diffusion in hydrogen combustion is also demonstrated in the publication of [PERSON] et al. [15]. They were able to represent the relevant regimes of diffusion, the evolution of the turbulences, and an accurate representation of the flame structure with low computational costs under consideration of molecular diffusion in hydrogen-rich jets. Concentrating on the impact of the chosen combustion as well as chemistry model [PERSON] et al. [7] showed, that the chosen chemistry has an impact on particle temperature. Moreover, the chosen combustion model influences the flame properties like temperature and flame velocity. [PERSON] et al. [16] clarified the effect of diffusion calculation and its influence on temperature distribution. Due to the modification of the existing fireFoam solver by considering different diffusivity of the respective components, a better agreement of the temperature and concentration distribution with experimental tests could be made. Moreover, it was found that considering the high diffusivity of hydrogen, the maximum temperature is close to the inlet. When the high diffusivity of H\({}_{2}\) was neglected, the maximum temperature formed along the centreline of the burner. Complementing the above study, [PERSON] et al. [17] published the derivation for the calculation of reactive flows considering different diffusivity of each component. To consider component-specific diffusivity, using the Burke-Schumann solution method, a so-called projection matrix was introduced. Using this method, it was possible to analyze, on the one hand, the diffusion between the conservation variables and, on the other hand, the reaction of the system, with the reaction kinetics exerting a significant influence on the flow field. In addition to creating a model to study a laminar hydrogen-nitrogen diffusion flame [PERSON] et al. [18], also conducted experimental tests. They found that the length of the hydrogen jet increases with increasing velocity as well as the maximum temperature in the combustion chamber. In addition, accounting for thermal diffusion resulted in a higher temperature overall.