This thesis presents a numerical and analytical investigation of the regenerative cooling system of a 500 N liquid rocket engine developed by the German startup DeltaOrbit. The engine was originally designed to operate under single-phase liquid conditions; however, it is currently undergoing experimental testing and study to transition to a multiphase operating regime. The present case study considers a fully liquid flow at the inlet of the cooling circuit, which, through heat exchange with the combustion chamber, undergoes complete evaporation, reaching the outlet of the cooling channel and subsequently the combustion chamber, in a gaseous state. Beyond the multiphase nature of the system, this work also addresses the effect of the spiralized configuration of the cooling channels, which was specifically designed to enhance local heat transfer.