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Well, you can use the stagnation temperature of air as the upper limit at least. (ie if the airflow was stopped to a standstill and all its energy went to heating it):
http://www.grc.nasa.gov/WWW/BGH/stagtmp.html

Doing a million very coarse simplifications, Mach 3.6 is about 1 km/s of speed, and air's specific heat capacity is about 1 kJ / (K*kg), we get the energy from motion to 5E5 J/kg and thus the temperature rise is 500000/1000 K or about 500 K. (Or 500 C temperature rise from ambient conditions). Assuming 230 K initial temp, which is -40 C, then a 500 C increase results in 460 C. That's the upper limit. In reality the heating is less, since the air is not stopped completely, the plane is shaped aerodynamically and we are interested in the heat of the structure, not that of air. The Cp of air at that altitude might be less though which would increase the temperature.
But the NASA page is better, it goes to more realistic calculations.

<blockquote data-quote="mz" data-source="post: 45720" data-attributes="member: 647">Well, you can use the stagnation temperature of air as the upper limit at least. (ie if the airflow was stopped to a standstill and all its energy went to heating it):http://www.grc.nasa.gov/WWW/BGH/stagtmp.htmlDoing a million very coarse simplifications, Mach 3.6 is about 1 km/s of speed, and air's specific heat capacity is about 1 kJ / (K*kg), we get the energy from motion to 5E5 J/kg and thus the temperature rise is 500000/1000 K or about 500 K. (Or 500 C temperature rise from ambient conditions). Assuming 230 K initial temp, which is -40 C, then a 500 C increase results in 460 C. That's the upper limit.&nbsp; In reality the heating is less, since the air is not stopped completely, the plane is shaped aerodynamically and we are interested in the heat of the structure, not that of air. The Cp of air at that altitude might be less though which would increase the temperature.But the NASA page is better, it goes to more realistic calculations.</blockquote>

[QUOTE="mz, post: 45720, member: 647"] Well, you can use the stagnation temperature of air as the upper limit at least. (ie if the airflow was stopped to a standstill and all its energy went to heating it): http://www.grc.nasa.gov/WWW/BGH/stagtmp.html Doing a million very coarse simplifications, Mach 3.6 is about 1 km/s of speed, and air's specific heat capacity is about 1 kJ / (K*kg), we get the energy from motion to 5E5 J/kg and thus the temperature rise is 500000/1000 K or about 500 K. (Or 500 C temperature rise from ambient conditions). Assuming 230 K initial temp, which is -40 C, then a 500 C increase results in 460 C. That's the upper limit. In reality the heating is less, since the air is not stopped completely, the plane is shaped aerodynamically and we are interested in the heat of the structure, not that of air. The Cp of air at that altitude might be less though which would increase the temperature. But the NASA page is better, it goes to more realistic calculations. [/QUOTE]

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