Explaining the Science of Heat Shield Tiles on the Space Shuttle

[James_Harford]

There is some possibility of confusion about what "steady state solution" means here. I would take it NOT as meaning uniform temperature everywhere and no heat flow -any form of insulation would delay reaching that state, but would not change the damage caused when it was reached. Rather, I would take it as meaning a uniform heat flux through the thickness of the tile, and therefore a linear temperature gradient through the tile.

Q_Goest has given the most detailed analysis on this question, which I believe is in good agreement with all of your points, except for the significance of the heat capacity of the tile. I found it very persuasive in spite of my earlier concerns on that exact point.

 

[Q_Goest]

Thanks AlephZero, I agree. Maybe one minor point:

the bad change is that when the external heat source is removed, the heat stored in the tile is conducted away in both directions - into the shuttle as well as back into the atmosphere.

The rate of heat transfer at the inner surface duiring 'steady state' (or any state during which the thermal gradient is aproximately linear as I've mentioned earlier) is always going to be higher than during this cool down period. We can be sure of this because the rate of heat transfer due to thermal conductivity is linearly proportional to dT/s at the inner surface. That's the slope of the temperature gradient at the inner surface. That slope only decreases as we go from a linear temperature gradient to one experienced during the transient. Agreed?

 

[AlephZero]

Agreed. The main point I was making was that the heat stored in the thermal capacity of the tile has to go somewhere, and it doesn't all go back out to the atmosphere just because that would a nice thing to happen.

I don't know enough about the shuttle tile system to estimate the thermal time constant (i.e the time for the system to approach a steady state condition) compared with duration of the heat input, so I don't know how relevant your refinement of the argument is in practice.