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I'm trying to numerically compute the macroscopic heat exchange in a simple system: a solid body surrounded in gas, initially at different temperatures. I, unfortunately, could not find any reference to estimate the thermal conductance at the interface. (Aka, the ratio between the heat exchange and the temperature difference on a unitary area, in Watts per square meters per Kelvin)

I'm only concerned with the diffusive effect, not with any radiative nor convective behavior.

Has anyone got any references for common scenarios? I'm looking for real-world values here. I guess the value at least depends on the material of the solid (Aluminium, Granite, Wood, etc.), the surface roughness, the gas (nitrogen, carbon dioxide, etc.), pressure and so on. Bonus points if anyone's got an idea on how much the heat conductivity varies with the system's parameters (like, how much thermal conductance increases if the gas pressure doubles.)

EDIT: Made the question not just about metal/air.

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  • $\begingroup$ Are you familiar with the concepts of natural- and forced convective heat transfer? $\endgroup$
    – Chet Miller
    Commented Jul 9, 2021 at 20:03
  • $\begingroup$ I'm confused by the votes to close under the "engineering" reason. The question isn't predicated on a practical application. The topic is thermal conduction. The goal is an accurate calculation. These aspects place the question far into the physics side of the spectrum, in my opinion. $\endgroup$
    – Chemomechanics
    Commented Jul 9, 2021 at 20:05
  • $\begingroup$ It has little to do with the solid surface, since the conductivity of air is significantly smaller. Is the air static or moving? That makes a difference. Pressure certainly does as well, but is just a linear scale factor for human-habitable conditions. $\endgroup$
    – Jon Custer
    Commented Jul 9, 2021 at 20:07
  • $\begingroup$ I see questions about the air movement and convection: As stated in the question, these phenomenons are out of scope. We could phrase the question as: What's the instantaneous thermal conductance? Considering a time interval small enough to make any air movement/convection neglectable. $\endgroup$
    – Marsya Kaustentein
    Commented Jul 10, 2021 at 8:05

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The (macroscale) thermal conductance of a fluid-solid interface is generally assumed to be infinite.

From Incropera & DeWitt's Fundamentals of Heat and Mass Transfer, 7th ed., §6.1.2, The Thermal Boundary Layer:

"Consider...an isothermal flat plate. [F]luid particles that come into contact with the plate achieve thermal equilibrium at the plate’s surface temperature. In turn, these particles exchange energy with those in the adjoining fluid layer, and temperature gradients develop in the fluid.

(Heat transfer across microscale and nanoscale gaps, where the gap size is comparable to or smaller than the molecular mean free path, is discussed in Zhang, Z. M., Nano/Microscale Heat Transfer, McGraw-Hill, New York, 2007, for example, but since you referred to an object "surrounded" by air, that's probably not relevant here.)

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  • $\begingroup$ Many thanks for the precise reference. However "assume the thermal conductance to be infinite" feels bold and may benefit from some justification. In particular, it implies that on a macro-scale, the interface does not have any effect, and the heat transfer just depends on the diffusive properties of the gas on the one hand, and the solid on the other. $\endgroup$
    – Marsya Kaustentein
    Commented Jul 10, 2021 at 8:18
  • $\begingroup$ Yes, that’s the implication. $\endgroup$
    – Chemomechanics
    Commented Jul 10, 2021 at 15:29

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