The SR-71 Blackbird has a top speed of just under 1000 ms at these speeds a significant amount of heat is generated on the surface of the airframe. Multiple design decisions were implemented to combat this. Large section of the inboard wings were corrugated as flat skins would split under thermal expansion. Fuselage panels were manufactured to fit loosely on the ground and would only properly align when the airframe heated up and expanded. However even with these structural measures a dynamic cooling system was required. Fuel was circulated in tubes under the skin of the aircraft to act as a heat sink. This also had the advantage of preheating the fuel before combustion. As a proof of concept calculation you are required use one-dimensional heat flux to find the speed with which the fuel would need to be pumped through the system to keep the skin of the aircraft at its operating temperature 300C. After passing through a shock the air in contact with the skin of the SR-71 is 500C and has a velocity of 125 ms 1. The average chord of the wing is 5m and is skinned in 10mm stainless steel. Given the operating pressure of the fuel system the cooling pipe has a 10mm internal diameter with a 5mm wall thickness. You can assume the fuel is pure octane which has a Prandlt number of 11.1, a thermal conductivity of 0.137 W m-K- and a dynamic viscosity of 714 x 10-6 kg/s m. First construct a one-dimensional thermal resistance diagram Find the required fuel velocity Comment on the limitation of this calculation (50 words)