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I'm trying to size the thickness of a shroud to encapsulate a payload on a small rocket. We're using carbon fiber pre-preg (k=6.83 W/m-K) and (per the aeroheating analysis based on the trajectory) the max heat rate is 908 kW/m^2.

The avionics housed inside the shroud are rated to 85 C (358 K).

How can I get an idea of what the thickness of the shroud needs to be to prevent overheating?

I tried to use Fourier's law for SS conduction through a plane wall as a crude first-order analysis to get an idea. So the outer temp. on the shroud moldline (To) is given by q"L/k + Ti. I've been picking inside temps. (Ti) that are some percentage of the max. temp the electronics can take (say, 50% or 179K) and a material thickness (ex. 1/8") and then comparing the predicted outer temp. with the glass transition temp. for the material. This doesn't seem like a very sound analysis, as it's also predicting overheating for basically every thickness I select.

Ideally, we could estimate the outer wall temp. and then calculate the thickness based on a desired inside temp. How should I approach this? I also don't have an estimate for h (heat transfer coefficient for convection) in this scenario.

I haven't had heat transfer in many years, so I think I'm feeling in the dark to some degree!

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# Heat transfer - aeroheating and material thickness

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