The question
The gas inside WD-01 is at about 3,250 K. Copper alloys lose their strength far below that. The usual answer is regenerative cooling: the propellant flows through channels in the wall before it is burned. Before we design those channels, we need the heat load.
How we computed it
The full inner wall, from injector to exit, with the gas state from D01. The heat-transfer coefficient follows the Bartz correlation, the standard first estimate for rocket nozzles, using viscosity, heat capacity and Prandtl number from NASA CEA. We assumed a hot-wall temperature of 800 K and also tried 600 and 1,000 K.
What we found
The heat flux peaks at 18.6 MW/m² right at the throat: almost 2 kW through every square centimetre, the power of a kitchen hot plate. In total 35 kW flow into the wall, and the long cylindrical chamber takes the largest share, 19 kW. Heated to 600 K, the 7 g/s of methane can absorb only 12 kW, about a third. Methane and oxygen together reach 76 %.
What it means
On paper, WD-01 cannot cool itself with methane alone. Small engines have this built in: the wall shrinks more slowly than the propellant flow that has to cool it. Shortening the chamber to L* = 0.5 m and cooling with both propellants would just cover the load. Film cooling and a radiation-cooled nozzle end are the other levers. Run D04 decides which ones WD-01 needs.
