Consider a slab made of two walls separated by air. Why do we need insulation material between the two walls. Air thermal conductivity is lower than most thermal conductivities of insulating material and convection cannot be an issue in the enclosed volume: hot air rises, so what? it won't go any further than the top of the cavity.
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You can think of thermal conductivity as a measure of how readily heat will flow through the material while it is stationary. The low thermal conductivity of air means that it takes a long time for heat to diffuse through an air pocket.
If the air is permitted to move, however, this intuition goes out the window. The air in contact with one wall gets warm and rises, and the resulting circulation causes it to be brought into contact with the other wall. In this way, the heat doesn't need to diffuse through the air, as it's being transported by bulk air flow.
Insulating materials such as blown fiberglass (or a wool sweater) are good insulators precisely because they trap many small pockets of air, which shuts down convection and forces the heat to flow diffusively. Once there's no convection, the low thermal conductivity of the air pockets makes the material a good insulator. You're right that the thermal conductivity of the trapping material is usually higher than the thermal conductivity of the air itself, but that's the (fairly modest) price we have to pay for killing the convection.
J. Murray
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10I seem to recall from physics class that this convection transfers so much heat that a wall of thickness $t$ is actually better than two walls of thickness $t/2-d$ with an airgap if thickness $d$. – gerrit Nov 22 '21 at 15:30
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2@gerrit so to translate into an example, a wall of solid plasterboard (!) would be better than 2 sheets and an air gap. I think that sounds obvious when written out, because we normally experience convection through air, so “imagine” it has poor insulating properties (when that’s not the case) – Tim Nov 22 '21 at 22:52
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If the air gap between the walls is wider than approximately 0.5 inches, the warm wall will heat the air, causing it to rise. The cold wall will cool the air, causing it to fall. This will set up a circulating air flow between the walls which transfers heat across the gap to a greater degree than expected. Insulation between the walls is a barrier to air circulation, which somewhat decreases the heat transfer across the gap.
Note that this is the exact reason that panes in double paned windows are spaced approximately 0.5 inches apart. At that spacing, the rising air and falling air in the gap between panes "fight" each other, and prevent air circulation from forming.
David White
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11Very interesting answer. I actually first had doubts about .5 inch figure - in Russia, where I come from, double windows have been ubiquitous for ages, but these are literally two single-pane windows in parallel, with a good 5-15 cm between them (2-6 inches). These are however being displaced by modern "European windows" - which I suppose lands merit to your theory. My current (French) window indeed has about 0.5 inches between the panes. – Roger V. Nov 22 '21 at 08:56
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6It's also why high-end windows are filled with heavy gas rather than (dry) air. It convects less. (My replacement windows have a plastic membrane between the two panes though killing convection is not its primary function, and they are filled with Krypton.) – JDługosz Nov 22 '21 at 15:29
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5@RogerVadim Well, the modern windows have more advantages (judging from Berlin where the same substitution is common): The enclosed gas is often Argon or Krypton with much lower thermal conductivity; the windows are essentially airtight, minimizing losses through airflow; and it's a single window. (The airtightness can cause a moisture problem but that's a different matter.) – Peter - Reinstate Monica Nov 22 '21 at 17:13
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2@RogerVadim double windows (even with a good distance between glass sheets and some convection between them) are stil WAY better than single windows in terms of heat loss. I heard (some years ago) somewhere in the northern Russia they even use triple windows (at -40C this probably helps). – fraxinus Nov 23 '21 at 13:55
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6@fraxinus interesting piece of trivia - a temperature of -40 does not need a C or F specification, as this is the point where both scales meet. – Mark Ransom Nov 23 '21 at 19:16
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1@fraxinus triple windows are common in my country too but we never reach -40C. They are just energy savers – undefined Nov 24 '21 at 08:07
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1I would love to learn more about the 0.5 inches figure, do you have any reference to share? – Benoit Esnard Nov 24 '21 at 08:24
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1@MarkRansom: Good to know. As a bonus, it cannot be Kelvin or Rankine either. :D – Eric Duminil Nov 24 '21 at 09:04
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1@fraxinus: for what it's worth, triple windows (like in three glass panes) are a standard these days for all modern construction in Russia. What they do in the northern Russia is a "three-layer sandwich panel" (тройной стеклопакет) which means three pockets of air trapped between four glass panes. – Quassnoi Nov 24 '21 at 15:32
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Complementing the excellent answers on convection; some heat can also transfer through radiation, if the internal surfaces of the two walls are not treated to counter this. Both the warm and the cold wall will radiate, but at different rates, and this results in an equalizing heat flow.
A quick calculation using [1] gives that a wall at 25 C will radiate 85 W/m2 to a wall at 0 C, if the walls have an arbitrary emissivity of 0.64.
Putting some IR-blocking material in-between the walls decreases this mode of heat transfer.
[1] https://www.engineeringtoolbox.com/radiation-heat-transfer-d_431.html
Anders Petersson
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1This is why some insulating materials have graphite mixed in the foam. It happens to be reflective for mm wavelengths and below. – fraxinus Nov 23 '21 at 13:58
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p.s. "and below" to be read below in photon energy, i.e. longer wavelengths – fraxinus Nov 24 '21 at 08:50
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I believe the "gold standard" for in-gap heat blocking material is called Reflectix, at least in the United States – Richie Frame Nov 25 '21 at 05:44
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1Yes indeed! This is one reason why aluminium foil is used as sarking (or to wrap hot food in): its very low emissivity means that even if it's hot, it emits minimal thermal radiation. The best wall insulation is actually a series of vertical foil-coated thin cardboard panels spaced about 10mm apart: the air limits conduction, the narrow gap limits convection and the coating limits radiation. But it's a real nuisance to install! – Chappo Hasn't Forgotten Nov 28 '21 at 05:39
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To take full account of the low thermal conductivity of air, it needs to be stationary.
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1This answer is more like a comment. Please add additional information and improve the post. – lee Nov 26 '21 at 15:20
Who could doubt that two separated walls would benefit from insulation between them? Who could claim that said anything about the nature of the insulation?
If it's clear that the thermal conductivity of air is lower than that of most substances, where is that published?
The claim doesn't sound unreasonable but if it's true, there should be tables used by several different kinds of engineers…
Where are those tables?
– Robbie Goodwin Nov 23 '21 at 21:26