Can our boffins help me with this - my A-level physics is rusty, and I do rely on getting a mental picture, which at present I can't, in this:

It's about what I think of as the speed of propagation of a new heat (or temp) wavefront thro a solid.

Say a cube of solid material is at uniform temp, and is highly insulated all round. A new heat source - say a hot plate that then maintains its steady high temp - is applied to one face of the cube. New heat flow immediately begins into and through the cube. The nearest part of the cube gets hot, but for a while the middle and furthest parts of the cube are unaffected - they don't 'know' yet that new heat is coming their way. How long does it take for the wavefront of new heat (i.e. higher temp) to work its way through to the other side?

In other words, what is the speed of propagation of a new heat (or temp) wavefront thro a solid?

Is this what they call Thermal Diffusivity (a)? Not quite, I think, because its units are not m/s (speed) but m2/s. That I can't get my head round.

I can see that the solid material's Thermal Conductivity (lamda) determines how quickly, for given delta-t, heat flows (J/s = W) in to fill say the first 1cm lamina of the solid cube.
I can see that the solid material's Volumetric Specific Heat Capacity vSHC (C) determines how quickly (s) that heat flow (J/s = W) will raise the temp of that lamina by say 1C, so that a delta-t is established between the first lamina and the next one, and the heat flow can be passed to the second one, and so on.

It seems to me that vSHC divided by Conductivity should give a result of time per 1cm lamina (s/cm). Or inversely, speed of propagation (cm/s - or m/s).
But apparently it doesn't - it gives m2/s.

Thermal conductivity lamda = W/mK =J/smK
J = lamda.smK

Volumetric specific heat capacity C = J/m3K
J = Cm3K

lamda.smK = Cm3K
lamda.s = Cm2

m2/s = lamda/C = thermal diffusivity a

Yeah I accept that. I didn't say 'wave', just 'wavefront' - the advancing edge of the ooze. A new ooze-edge advances at a speed of m/s. The distant part doesn't 'know' that an ooze is heading its way till well after the new ooze begins.

If you are looking at this for practicable building design, Tom, then thermal diffusivity is simply thermal conductivity, divided by volumetric heat capacity (which in turn is the product of SHC and density)

It might be easier to think of it in terms of decrement delay and how that relates to decrement factors ie the rate of heat transfer and the attenuation of the swings about the norm.

You can use thermal admittance as the basis for evaluating the delay - if you fancy a bit of spreadsheet work, I think the concrete centre has a little excel spreadsheet based tool ( I think it was Arup who set it up initially)

The calculation methodology is actually set out in BS EN ISO 13786:2007 Thermal performance of building components. Dynamic thermal characteristics. Calculation methods

Doing it long hand in what if scenarios is a right pain though. Just keep in mind that increasing thickness increases the delay and dampens the swings and that where you place insulation is hugely important - EWI can significantly increase delay compared to IWI for a similar u value

regards

Barney

Posted By: fostertom A new ooze-edge advances at a speed of m/s.

I think that concept is mistaken and therefore not helpful.

If you were to do a finite element calculation of heat flowing down an insulated rod when you instantaneously raise the temp of one end, the time taken for any temperature rise at the other end would depend only on how tiny you were prepared to make the finite elements, and how many decimal places you were prepared to calculate to. With infinitely small elements and perfect accuracy the arrival of heat at the far end would in theory be instantaneous, although infinitely small!

I don't have the physics to know what the limit is in practice, but my money is on it being way faster than any timescale of interest in buildings

Posted By: barneykeep in mind that increasing thickness increases the delay and dampens the swings and that where you place insulation is hugely important

That agrees with my qualitative understanding. I'm trying to grasp 'thickness increases delay' by transforming it into speed of propagation, and deriving that from resistivity and vSHC. 'Dampens the swings' (decrement) to follow.

That's the trouble - hoping for something I can picture! I struggled totally with A level Maths, can't understand why because it's all about shapes and patterns, should thrive on it

Tom, AIUI the thermal diffusivity relates to both the velocity and dampening factor of the heat wave. In fact diffusivity is proportional to the ratio of velocity to dampening factor.

Imagine two materials, both conduct a heat wave at same velocity, but one has more dampening factor, due to greater SHC. That would be the one with lower Thermal Diffusivity.

This means velocity is not proportional to Thermal diffusivity alone . That’s also why the units are different.

To disappoint further, I don’t believe a given material propagates all thermal waves at the same speed, I think it depends on the wave frequency. EG seasonal variations propagate at lower velocity than day-night variations, but get dampened less.

Google turned up this paper, ignore all the heavy maths and just scroll down to eqns 9 10 and 11:

http://physlab.lums.edu.pk/images/2/2d/Bodasref.pdf

Posted By: barneygo and look at the "Dynamic Thermal Properties Calculator"

Thanks - looks mainly about in-out heat flow to massiveness 'within the room' and only slightly about uni-directional heat flow? I will read Will's paper first then try it out on yours.

I think the oil slick analogy is a bit misleading as oil has surface tension so there will be definite edge to the blob.

On the other hand, the idea that the first infinitesimal temperature rise will propagate “instantly” (though at less than the speed of light presumably (perhaps at the speed of sound in the material?)) doesn't feel right, either.

Had an unsociable breakfast reading Will's paper - fascinating, tho I couldn't follow the maths (wish v much I could).

So velocity of propagation is not fixed for ea material, but depends also on frequency of the oscillation. And a period as long as one year still counts as an oscillating wave.

Posted By: mike7the sluggish and momentumless flow I saw in seasonal heat store simulations. This contrasted with the notion that seemed to be abroad at the time of sprightly waves of heat traveling in to heat stores and obligingly bouncing back out again in the required direction at the right time with worthwhile amplitude...

Low frequency means low velocity but also small damping of the wave. So a thermal wave in subsoil resulting from summer input of heat at a point 6m deep would indeed travel slowly, with small(ish) damping, perhaps at the '1m per month' rule-of-thumb quoted by the PAHS/AGS guys, and would still be a bit peaky when it arrived 6 months later at the underside of the uninsulated floor slab (doesn't have to be peaky to be useful, but peakiness is additionally exploitable).

By contrast, a period of 24hrs wd mean high velocity and high damping, which wd explain the disappointing benefits of trying to use thermal mass by just sticking lumps of it in the room, and by receiving solar radiation thro windows onto heavy floor etc.

The other interesting hint, two thirds down p529: thermal waves can be superposed. What? cd that mean that two thermal waves superposed cd create amplitude (temp) peaks higher than the amplitude (temp) peaks of either original wave? Could this be a way of concentrating heat into higher temps, like a heat pump? I was told 'no' on that some time ago, yet here it is again ...

Getting back to the units of diffusivity being m^2/s, FWIW I think this implies that should you double the linear scale of a store, you quadruple the timescale it operates over.
I should like to participate more in this thread but sadly my wits seem to have suffered a decrement of 50% over a period of 40 years or so.

Posted By: djh

Posted By: fostertomSo velocity of propagation is not fixed for ea material, but depends also on frequency of the oscillation.

Yes, that's true for pretty much all waves. It's why we see rainbows, for example

Yeah, tying that in with lots of things now - magic! (or science, possibly)

V gd. Two things:

If "The speed of light is always 3.00e8 m/s", means the speed of wave propagation thro the electromagnetic field is fixed.
So why is the speed of many other waves (incl thermal waves) thro their respective fields/media, variable depending on frequency?
Someone suggested it's the relationship of wavelength to length of organ pipe - i.e. how many wavelengths in play, in the given system?

And " Heinrich Hertz, one member of the Hertz family that made many important contributions to physics" - baked beans?

Wot, when the field is pulled by gravity or something?
And how about the baked beans?

Ah of course, so why do they say 'speed of light' - means in space?