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Forgive my layman, non-physicist terminology used here. Hopefully I'm not too much of a caveman to express myself properly.

What does thermal conductivity actually express? Is it measuring the amount of heat that transfers through a material? Or the speed at which the heat transfers? Or some combination of the two? Or something else?

For example, if I have a wall with such-and-such thermal conductivity and a heat source on one side, what does thermal conductivity actually tell me for the amount of heat that will be transferred to the other side, how long that will take, and so on?

Edit: if thermal conductivity is the speed of heat transfer, what am I to make of the fact that dense materials like concrete and compressed earth blocks have a high thermal conductivity (≈1.5) relative to dedicated insulation materials (≈0.04), yet heat transfers through them slowly--this property being explicitly utilized in certain applications, in fact, such as passive solar design.

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  • $\begingroup$ Wikipedia is always your best friend: en.wikipedia.org/wiki/Thermal_conductivity $\endgroup$
    – Mobin
    Apr 10, 2015 at 22:40
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    $\begingroup$ Wikipedia isn't helping me much. That page doesn't seem to answer my question in a way that I understand. Maybe I just need it explained like I'm 5. $\endgroup$
    – iLikeDirt
    Apr 10, 2015 at 22:40
  • $\begingroup$ I guess it depends on what you mean by "very high". They're much higher than gasses, but much lower than metals. Earth isn't used sometimes because it's a fabulous insulator. It's used because it's cheap and you can use a bunch to get the insulation to the level you want. It might be cheaper to build a 2-foot earthen wall than a 1-inch fiberglass wall. $\endgroup$
    – BowlOfRed
    Apr 10, 2015 at 23:07
  • $\begingroup$ Also, there's nothing to say that you can't use both. You can use a lot of earth as part of the thermal system, then add in some other insulation as well. $\endgroup$
    – BowlOfRed
    Apr 10, 2015 at 23:15
  • $\begingroup$ the constitutive equation is $$ \mathbf{q} = - k \, \nabla u \ $$ where q is the J/(s*m^2) (the heat flux) u is in K and k is in W·m−1·K−1 then we have through the coninuity equation that the div of the flux is the volumetric density of q in which the specific heat may appear but really Q=mcdeltaT $\endgroup$
    – ChemEng
    May 14, 2020 at 23:01

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Thermal conductivity measures the speed at which heat energy travels through material.

That's different to the speed at which changes in temperature travel through material, which is driven by a combination of thermal conductivity and thermal mass.

So, to use your example, concrete has a high thermal conductivity: it will lose heat energy quite quickly, so a hot thing inside a concrete box can cool down quite quickly. However, concrete has high thermal mass: it takes a lot of energy to raise its temperature by 1 Kelvin. So even with heat going into it quickly, its temperature will rise slowly.

That's why concrete and earth walls are used in some passive solar designs: not necessarily for their insulation properties, but for their properties as a heat buffer: they can absorb a lot of heat for relatively low changes in their own temperature, and radiate it back out again. That gives you a wall surface with a fairly steady radiant temperature, which feels a lot more comfortable than a surface with a highly variable radiant temperature; and it gives you a huge buffer that allows you to store solar energy in the day and release it at night, thus giving you cooling during the day when you need it, and heating during the night when you need it.

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  • $\begingroup$ Ahh, it all makes sense now. $\endgroup$
    – iLikeDirt
    Apr 11, 2015 at 5:05
  • $\begingroup$ "the speed at which ..." is not quite right. You should say "the rate at which". $\endgroup$ May 15, 2020 at 23:26
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It represent the speed actually. it is defined as:

"The amount of energy that is transferred from A to B where $AB=1meter$ and difference between the temperature of point A and B is 1 kelvin, in each second."

for example the the thermal conductivity of wood is about 0.4 . it means if you have a wood with a length of 1 meter and and $\Delta(\theta)=1 degree$ (of both end of the wood) then 0.4 joules will be transferred in each second, from one end to another.

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  • $\begingroup$ Edited my original question to reflect my confusion if thermal conductivity is simply the speed of heat transfer. $\endgroup$
    – iLikeDirt
    Apr 10, 2015 at 23:05
  • $\begingroup$ @iLikeDirt you have to see that a single number cannot gives us much of a detail. yes the earth block's thermal conductivity is about 1.5 while the water's about 0.6. it means that heat transferred much faster in the earth than the water. or air's is 0.025 . it means the air is too bad at transferring the heat because it transfer lower energy in one second. see that it is not only the "Speed" of transferring, but the amount of energy that is transferred in one second. if you didn't get it let me know to explain it more. $\endgroup$
    – Mobin
    Apr 10, 2015 at 23:06
  • $\begingroup$ Wait, first you said it was the speed, and now you're saying it's some combination of the speed and something else. I am kind of confused. $\endgroup$
    – iLikeDirt
    Apr 10, 2015 at 23:25
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    $\begingroup$ @iLikeDirt Yes , it's heat per meter per second per degree! it depends on all of them.if you stand in front of a fire you will feel the heat very quickly. but the heat is just very low! it means in each second a little amount of heat in transferred by the air. see we can define two kind of speed. probably you are thinking about the amount of meters the heat is traveled in one second . but thermal conductivity is not that! it's the amount of "jouls" that transferred in one second. we divide the power by the meter because of that. the speed is for the energy, not the speed that the energy is spr $\endgroup$
    – Mobin
    Apr 10, 2015 at 23:32
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One of the best ways to explain concepts like this are to use labelled diagrams, such as

enter image description here

with a very nice explanation from the CBFT blog page, with a nice definition:

When the temperature of one surface of a solid material is higher than another, heat will move through the material. Depending on the characteristics of the material, this conductive heat transfer may be slow or it may occur quickly. The rate of heat transfer is defined by the coefficient of thermal conductivity.

Essentially, thermal conductivity is how fast will heat from its source pass through the material - if the material is thicker, then it will take more time to conduct through.

It's reciprocal is thermal resistance

(not a 'caveman' question at all!)

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  • $\begingroup$ Edited my original question to reflect my confusion if thermal conductivity is simply the speed of heat transfer. $\endgroup$
    – iLikeDirt
    Apr 10, 2015 at 23:05
  • $\begingroup$ @iLikeDirt it could be that as there is a lot more 'stuff' in denser materials, the heat energy gets sapped quicker as it conducts through the material. $\endgroup$
    – user77400
    Apr 10, 2015 at 23:12
  • $\begingroup$ Actually, it is stored. A dense material "saturates" with heat as the heat transfers through it (due to its density I guess) while a lighter material is not able to store much heat in it as the heat passes through. $\endgroup$
    – iLikeDirt
    Apr 10, 2015 at 23:21
  • $\begingroup$ Therein lies the answer to your edit-added question - if the heat is stored, then it is not going to easily conduct to the other side. $\endgroup$
    – user77400
    Apr 10, 2015 at 23:24
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    $\begingroup$ Something stored is not moving - so the heat energy stored within the concrete is not conducted through the concrete. The article Guide to Thermal Properties of Concrete and Masonry Systems may be of interest. $\endgroup$
    – user77400
    Apr 10, 2015 at 23:53
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The reciprocal of thermal conductivity is thermal resistivity (from this source). In analogy to ohm resistance, where the resistance depends from both the current flow and the potential difference, you are right saying that it is showing "the amount of heat that transfers through a material" and "the speed at which the heat transfers".

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I believe your confusion is caused by mixing two different measures of conductivity. Steady state conductivity and transient conductivity.(also referred to as dynamic heat flow)

Steady state is the easy concept and is generally what is intended when talking about conductivity. Steady temperatures are applied to each side of a material(one side warm, one side cool) and then you wait for an extended time(hours, days, weeks) for the material's internal temperatures and heat flow to settle into a constant steady state. At this point you calculate the energy flowing(usually in watts) across the material per degree of temperature difference. This can be for a total for a complete object or per unit of area and thickness for a material property. (note that you could also use steady power input and then measure the temperature difference after waiting for it to settle, just two sides of the same equation.)

Transient conductivity is the heat flow from momentary changes in temperature or power, and this can have several forms depending on what you are engineering, flow from side A, flow to side B, or some combination. This transient effect is seen in your example of a solid concrete wall where the material has a moderate steady state conductivity but also a large heat capacity and so thermal changes on one side take substantial time to be noticed on the far side. This heat capacity mechanism will tend to make the transient conductivity seem higher than steady state when measured on the near side(side with change) and lower when measured on the far side(side without change), it will also tend to cause delay or lag in temperatures.

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Suppose we have flat plane of some material through which heat is passing in the perpendicular direction. For example it is a layer of material placed in front of a heater, or something like that. Let the $x$ direction be perpendicular to this plane.

Let $J$ be the amount of heat energy passing through the plane, per unit area of the plane and per unit time. So in dimensional terms this $J$ is a power per unit area. It is also often called a flux. Let $dT/dx$ be the temperature gradient at the surface. Then $$ J = - \kappa \frac{dT}{dx} $$ where $\kappa$ is the thermal conductivity. If you are unfamiliar with this notation then for a uniform flat slab of material you can also write it as $$ J = - \kappa \left( \frac{T_{\rm out} - T_{\rm in}}{w} \right) = \kappa \left( \frac{T_{\rm in} - T_{\rm out}}{w} \right) $$ where $w$ is the thickness of the slab.

Therefore thermal conductivity is the amount of heat flux per unit temperature gradient. Think of the temperature gradient as providing a slope, and the heat wants to flow down this slope. It doesn't all rush down in an avalanche because the material (with property $\kappa$) is resisting the flow a bit. But neither is the flow totally blocked by the material. The material has a propensity to allow the heat to go through. This propensity we call thermal conductivity.

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