An extensive investigation of multi-nozzle with various heights is done for enhancing the fuel mixing and distribution in supersonic combustion chambers of scramjets by using Computational Fluid Dynamics. Fuel injection and mixing play a crucial role in many industries, including automotive. This study examines the mechanism of hydrogen fuel jet mixing when injected through a multi-nozzle with varying heights in the combustion chamber of a scramjet. The impact of different injector height configurations on supersonic cross-flow is analyzed through computational fluid dynamics, and the flow and fuel mixing are evaluated to determine the most efficient fuel injection setup. A comparison is made between the proposed multi-jet configurations and simple multijet configurations to identify the primary hydrodynamic and mixing benefits of multi-jet configuration with different heights. The findings indicate that the use of multi-jet injectors with different heights decreases the circulation factor and improves fuel mixing downstream of four jets by 40 %.