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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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    $\begingroup$ I've removed a number of comments that answered the question, and replies to them. To answer a question, post an answer. $\endgroup$
    – rob
    Commented Nov 21, 2021 at 22:08
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    $\begingroup$ convection cannot be an issue in the enclosed volume - did you ever read as to why heating systems that use convective panels ("radiators") place them underneath windows? $\endgroup$
    – Caius Jard
    Commented Nov 22, 2021 at 17:08
  • $\begingroup$ @PcMan This comment contains much more sass than it does helpful information. $\endgroup$ Commented Nov 23, 2021 at 19:15
  • $\begingroup$ The actual wording of the specific Question is… uh… not much use, anyway… 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? $\endgroup$ Commented Nov 23, 2021 at 21:26
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    $\begingroup$ That material between walls is also for acoustic insulation. $\endgroup$
    – user11153
    Commented Nov 24, 2021 at 9:15

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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.

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    $\begingroup$ I 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 $d$. $\endgroup$
    – gerrit
    Commented Nov 22, 2021 at 15:30
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    $\begingroup$ @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) $\endgroup$
    – Tim
    Commented Nov 22, 2021 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.

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    $\begingroup$ Very 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. $\endgroup$
    – Roger V.
    Commented Nov 22, 2021 at 8:56
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    $\begingroup$ It'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.) $\endgroup$
    – JDługosz
    Commented Nov 22, 2021 at 15:29
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    $\begingroup$ @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.) $\endgroup$ Commented Nov 22, 2021 at 17:13
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    $\begingroup$ @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). $\endgroup$
    – fraxinus
    Commented Nov 23, 2021 at 13:55
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    $\begingroup$ @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. $\endgroup$ Commented Nov 23, 2021 at 19:16
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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

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    $\begingroup$ This is why some insulating materials have graphite mixed in the foam. It happens to be reflective for mm wavelengths and below. $\endgroup$
    – fraxinus
    Commented Nov 23, 2021 at 13:58
  • $\begingroup$ p.s. "and below" to be read below in photon energy, i.e. longer wavelengths $\endgroup$
    – fraxinus
    Commented Nov 24, 2021 at 8:50
  • $\begingroup$ I believe the "gold standard" for in-gap heat blocking material is called Reflectix, at least in the United States $\endgroup$ Commented Nov 25, 2021 at 5:44
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    $\begingroup$ Yes 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! $\endgroup$ Commented Nov 28, 2021 at 5:39
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To take full account of the low thermal conductivity of air, it needs to be stationary.

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    $\begingroup$ This answer is more like a comment. Please add additional information and improve the post. $\endgroup$
    – lee
    Commented Nov 26, 2021 at 15:20

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