In this work, a regenerative cooling system for a hybrid rocket engine of 300 N thrust was tested and numerically simulated. The tests were run in the Space System Laboratory of Hokkaido University in Japan, using a combination of liquid oxygen and HDPE (high-density polyethylene). The cooling system consists of 3 helicoidal channels using the oxidizer as a coolant to avoid graphite nozzle erosion. The numerical model developed in ANSYS - fluent, is based on an iterative process using a 3D simulation of the cooling channels and a 2D simulation of the nozzle's wall. In particular, an empirical relation was extrapolated from the experimental data to estimate the average number of bubbles formed in the channels.