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What is a rough cut figure I could use to determine what the thermal conductivity of 10mil and/or 20mil of air sandwiched between two plates (perfectly conducting)?

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I understand that convection dies at a certain point radiation and conduction takes over since the air is not moving much if at all when there are small gaps. At what point does convection stop with a variable gap?

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  • $\begingroup$ Are we talking about two horizontal-plane plates separated vertically or two vertical-plane plates separated horizontally? (It makes a difference to the "at what point does convection stop" question.) $\endgroup$ Apr 27, 2022 at 19:44
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    $\begingroup$ Horizontal Plane with 10mil air between them $\endgroup$ Apr 27, 2022 at 19:49

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This paper reviews the measurements available at the time of the thermal conductivity of air, and comes up with a typical value of $2.2\times 10^{-2}\,\mathsf{W}/\left(\,\mathsf{m}\,\mathsf{K}\right)$. From kinetic theory, one would expect the exact value to depend on the flux density of molecules and on the mean free path, i.e. on temperature and pressure.

Since the configuration of interest has two horizontal-plane plates separated vertically, the type of convection at issue is known as Rayleigh-B'enard convection, and one would expect the convection to shut down when the Rayleigh number drops below a critical value of $1\,708$.

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