Thermal compound conductivity choice...rule of thumb? Need to do the maths?

[showman]

But in this thread we are talking about conduction, not convection. Conduction happens in small spaces where the air is not free to move. Thermal conductivity is a physical constant of air and does not change when the air is in pockets or otherwise. In fact, aerogel has a higher thermal conductivity than air because the thermal conductivity of the aerogel material is greater than that of air. (For example, air has a thermal conductivity of 0.024 W/m-K, while typical solid materials are in the order of 100 times more conductive than that.)

And if you actually click on the link you'll see that the thermal conductivity of that particular aerogel given as an example is 0.005 W/m-K. Much lower than the air's 0.024. This has nothing to do with convection, why even bring it up?

If you have two dissimilar metals in perfect molecular contact (for example soldered or brazed), there is not, in fact, a sharp drop of temperature at the interface. The temperature gradient is smooth and continuous, although there will be a sharp change in the gradient at the interface due to the different thermal conductivities.

It is very well known that the interface itself has thermal resistance, first random work from google https://www.mdpi.com/2073-4360/12/10/2409. Not metal-metal, but the idea is the same.

[IanB]

And if you actually click on the link you'll see that the thermal conductivity of that particular aerogel given as an example is 0.005 W/m-K. Much lower than the air's 0.024. This has nothing to do with convection, why even bring it up?

Very well. I stand corrected. I did not realize aerogels fall into such a special category. See the comment I made before:

If you reach low enough pressures, or small enough scales where the mean free path of gas molecules becomes significant, then different theory is needed, and I am not familiar with this area. It is unusual, and not normally encountered in everyday engineering.

I mention convection, because preventing convection is an important reason for the performance of all air-pocket based insulating materials, including aerogels.

If you have two dissimilar metals in perfect molecular contact (for example soldered or brazed), there is not, in fact, a sharp drop of temperature at the interface. The temperature gradient is smooth and continuous, although there will be a sharp change in the gradient at the interface due to the different thermal conductivities.

It is very well known that the interface itself has thermal resistance, first random work from google https://www.mdpi.com/2073-4360/12/10/2409. Not metal-metal, but the idea is the same.

If you have dissimilar materials in contact, like polymer in an injection mold, they are not molecularly bonded (otherwise you would not get the polymer out of the mold). When there is physical contact, but not molecular bonding, then yes, there is an interruption to the heat transfer path at the interface. Granted.

[T3sl4co1l]

I mean, there's a small change at the interface between materials -- but it's very small indeed, and microscopic in nature: grain boundaries between crystals, and different types of crystals (e.g. pure iron to brass to copper, etc.).

On a macroscopic scale, these all average out as the bulk conductivity of the material.  You get a very small anisotropy with directional solidification (actually, I wonder how much, for what kinds of materials; I assume it's *something*), more in single-crystal materials (take graphite for an extreme case, ~5 W/(m.K) thru-plane, >2000 in-plane).

Basically nothing to worry about, interface is dominated by the boundary layer (i.e., fill it with grease to be sure), and bulk conductivity and heat equation applies.

Tim

[showman]

If you have dissimilar materials in contact, like polymer in an injection mold, they are not molecularly bonded (otherwise you would not get the polymer out of the mold). When there is physical contact, but not molecular bonding, then yes, there is an interruption to the heat transfer path at the interface. Granted.

This is a strawman argument. There is nothing about getting the polymer out of the mold. It is a simulation paper (i.e. idealistic case) where there is as perfect molecular contact there can be.
I'll copy the image here that actually shows the structure and the temperature plot.

Also the change in this particular case is not insignificant, but almost 100 degrees.

[IanB]

The paper addresses in great technical detail the same thing that I wrote. I am glad we are agreed.

[showman]

The paper addresses in great technical detail the same thing that I wrote. I am glad we are agreed.

Not sure about that. First I think you overestimate/emphasize the importance of "bonding". You don't need any attractive interaction to transfer heat. As you yourself pointed out earlier, energy is transferred by collisions (does not really matter if its gas, liquid or solid), so it is the repulsion that matters the most. Yes, attraction matters too, but it is secondary.  Secondly if you believe the same effect occurs at a solder-copper interface, yes we agree, but I don't think you do because "bonding". I'm pretty sure that you are sure that electrical energy reflects at impedance discontinuities, but for some weird reason it seems unbelievable that heat energy can reflect at atomic structure discontinuities.

Non-infinite thermal conduction in crystalline materials like metals occurs (leaving electrons aside for now, but similar arguments as below will apply as well) because phonons which transport energy collide with each other. When they travel inside a solid, the motion is essentially determined by the mechanical, if you will, characteristic impedance of the material, normally called the phonon dispersion relation. This characteristic impedance is different for every material. Now when you put two materials together, even if they bond very strongly, for the sake of argument let's say even more strongly than the atoms within the two materials themselves, there is an impedance discontinuity at the boundary which will reflect the phonons back to the material it came from. The only way to make it more efficient to transport energy across the interface is to impedance match the two materials, but just stronger bonding of the interface does not do it, at least not to the degree that all reflections are removed. In fact very strong bonds (as well as very weak ones) at the interface likely increase the mismatch so there are more reflections (larger temperature drop).

Note that whereas this effect is also real in a solder-copper interface, it can also be somewhat (but not completely) impedance matched, when for example you don't have an atomically sharp interface, but some diffusion of tin into copper/vice versa that makes the interface/material properties variations more smooth.

[IanB]

Thanks for the information about phonons.

I have never delved that deeply into heat transfer at the microscale and the associated physics. There also appears to be a difference between metals and non-metals, with electrons playing a role in heat conduction in metals.

A subject for further reading when I have spare time.

[showman]

Thanks for the information about phonons.

I have never delved that deeply into heat transfer at the microscale and the associated physics. There also appears to be a difference between metals and non-metals, with electrons playing a role in heat conduction in metals.

A subject for further reading when I have spare time.

Yes, at room temperature the electronic thermal conductivity is typically much larger in metals than the lattice (phonon) thermal conductivity, but to actually handle that there is really no way around quantum mechanics so things get significantly more complicated. Also because of that complexity I don't know if anyone has done similar calculations as above with both electrons and phonons. Whereas the same argument applies about discontinuities, it could be that the electronic part is less sensitive to that in which case the temperature drop could be even smaller than with the somewhat impedance-matched one for the solder-copper case (but still non-zero).

[T3sl4co1l]

Yeah, phonons are just the quanta of sound (acoustic) waves; the wavelengths relevant for thermal purposes are quite high indeed, and easily scatter, and absorb and emit spontaneously (as you might assume from being thermalized..!), so it's not like you're going to hook up a piezo disc and listen to its temperature; but the physics is the same as regular LF acoustics.  So we can think of it in terms of impedance matching between bulk substances of varying speed-of-sound and density.  (Also, not that these parameters are exactly the LF values either; I believe there's some skew to them, approaching cutoff?  And of course, the upper cutoff is given by, essentially, the mode where every other atom in the crystal is moving oppositely, the spacial Nyquist limit if you will.)

(Which, such a cutoff is obvious enough in solids, and, I believe was sufficient to explain the heat capacity of materials?  But applying the same reasoning was quite the quandry for EM radiation.  Circa turn-of-the-last-century.  The same wavelength vs. degrees of freedom argument, applied to the EM field, leads to the "ultraviolet catastrophe" because there's simply no such limit to the classical EM field: the further up you go in frequency, the more modes fit in a given volume of space, and those modes should all fill equally with thermal energy (equipartition theorem).  Setting an energy-based cutoff, and solving a fairly nasty integral, delivered the black-body spectrum perfectly; but no one quite believed the method, or really understood why it worked.  IIRC, Planck himself disapproved of QM and always considered his trick a hack; mind, this was at a time when convenient hacks were popular in physics, Rutherford's "plum pudding" model, or Bohr's (literal) atomic orbit model of hydrogen, for examples.  It took some decades before we had QM developed well enough to reasonably believe, yeah this weird shit seems to actually be what's going on, and to justify those hacks via direct solution or suitable approximation from the equations of motion, or state.)

Tim

[showman]

I think it happened in reverse order, so Einstein and Debye essentially used Planck's EM theory to derive the roughly correct heat capacity for solids thereby further validating QM. The key for both is not the upper cutoff, but the quantization of energy itself. So for phonons it is the lower cutoff that really matters. I.e. classically they can have as low energy (above the ground state, which classically is 0, but in QM not) as you wish, but quantum mechanically as you approach 0 K the degrees of freedom start to be confined to their ground (lowest energy) states as you no longer have sufficent (thermal) energy to excite those, so equipartition does not hold any more and the heat capacity drops to 0 as opposed to the classical 3kB. Or in other words if you add a tiny amount (below the Planck's constant times the phonon frequency) of energy to a classical crystal at 0 K, its temperature will rise by a tiny amount, but trying to add the same small amount of energy to a quantum crystal will result in nothing. For light I think (but not quite sure) it is roughly the same argument, so at small wavelengths the gaps between energy levels get increasingly large so essentially those degrees of freedom or modes get frozen out as you don't have enough energy to excite those beyond the ground state as opposed to the classical case where the energy is not confined to specific levels.

[helius]

The performance of a thermal paste is not only about the R_k of its filler and the amount of oil used. Even if the oil fraction gets reduced to zero, a uniform powdered ceramic like zinc oxide can't conduct heat nearly as well as its bulk solid form, because there is a limit to the density by which uniform spheres may be packed of 63%. To get high performance from a thermal paste, densification must be used, which combines different particle sizes in the necessary ratios to achieve a nearly 100% packing density.

TechIngredients did a good video about this years ago: