The entrance of the space module into atmosphere is one of the very critical phases of any space mission. Due to the formation of bow shock (Detached) in front of the module, the air temperature drastically increases to thousands of Kelvin. One suggested in order to find the amount of heat transfer to the space module at the reentry phase, we can set up an experiment on the ground with a scaled model in the wind tunnel. The proposed scaled model is 1/x times and is located in a wind tunnel with a maximum air velocity 100 times less than the actual velocity of the module. The density of the air at the reentry zone is almost 1000 times less than air density at the sea level, where the wind turbine is located. The see level air Prandtl number is approximately the same as the reentry zone. But the dynamic viscosity of air at the reentry condition is almost 3.59 times of the sea level air viscosity. The Thermal conductivity of air in the reentry condition is 4.356 times the sea level condition.
In the wind tunnel for the air temperature difference of 100°C between air and the scaled model, the energy transfer due to the heat was measured to be about 400W. At the reentry condition with 1500C Temperature how much is the energy transfer due to the heat to the module? For consistency modeling find the 1/x scaling ration.