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I want to calculate the contact conductance between two surfaces that have a thin layer of air (on the order of micrometers) between them. A quick literature review shows that the heat transfer coefficient between the surfaces may be calculated with:

$$ \Lambda=\frac{K}{d+g_1+g_2} $$

Where:

  • $Λ$ is the heat transfer coefficient
  • $K$ is the thermal conductivity of the gas
  • $d$ is the mean thickness of the gap
  • $g_1$ and $g_2$ are the temperature jump distances of the surfaces (in my case $g_1 = g_2$)

According to Kennard (pp. 311-315), the temperature jump distance may be calculated with:

$$ g=\frac{2-\alpha}{\alpha}\frac{4c}{\gamma+1}\frac{K}{\eta C_v}L $$

Where:

  • $α$ is a constant that depends on the surface properties
  • $γ$ is the ratio of specific heats of the gas ($C_p/C_v$)
  • $K$ is the thermal conductivity of the gas
  • $μ$ is the viscosity of the gas
  • $C_v$ is the specific heat at constant volume
  • $L$ is the mean free path of the gas molecules

Kennard assumed that the gas behaves as an ideal gas for these calculations. My problem involves two surfaces that are relatively hot, around 900 °C; the contact pressure is around 100 MPa; and the mean gap is between 1 and 20 μm. Is it reasonable to keep the ideal gas assumption under these conditions?

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