Posted By: mike7The other guy studied the frequency of car rental.

He should have tried harder!

Posted By: fostertomSo velocity of propagation ... depends also on frequency of the oscillation

What would a step change in amplitude of input count as? i.e. steady-state conditions (after equilibriation) both before and after the change in input amplitude, e.g. suddenly raising the maintained temp of the hot plate that contacts one side of the test cube.

A single temp wavefront would travel thro the cube (as described early in this thread) - at what speed? Its initial steepness would flatten as it progressed - decrement.

Is a step change like an infinitely long, or an infinitely short wavelength? If like infinitely long, the wavefront would travel slower, with less decrement; if like infinitely short, it would travel faster, with more decrement.

This shows temperature profiles at depth over a season for soils of different diffusivities (figs9,10,11):-
http://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CCgQFjAB&url=http%3A%2F%2Farchbps1.campus.tue.nl%2Fbpswiki%2Fimages%2F6%2F6a%2FH3.pdf&ei=_U6UUMKXErSN0wWq-IHIBQ&usg=AFQjCNEgV00IvZpvoCPrvZF-HxYNYpXK0g&sig2=EoTSPXiMu_ngfRrSGCpBhw

Interesting to see how the diffusivity affects the penetration of the seasonal variation.

Although these results are for a season and for soil, the scale factor of m^2/s can be used to translate the results for any time period. Eg. if you wanted to see the result for a temperature cycle time of 1 hour rather than a year then the distance axis would be shortened by the sq root of 8760 (hrs in a yr) = 93.6, so each of their metres would become about 11 mm.

Tom, I tried to email you a spreadsheet for simulating the step change you're interested in. It's beyond me to post it here. Did you get it?

Posted By: fostertomIt 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.

Granted your 'wave' must have a speed, but suppose the speed varies inversely with distance from the origin. That would give you m/s divided by 1/m, which gets you to m^2/s. Any help? I think we need a proper boffin here.

(I use the term 'boffin' to describe somone with profound, admirable knowledge and understanding of maths and science, without implying any defect or lack of personality, humanity or social competence so as to make myself feel better about my own inadequacies in those achievements.)

I was born within acne - it's in east London.

During a break from stick whittling I found this:-

Although waves are ubiquitous in nature it is difficult to give a precise and unambiguous definition of what a wave is. Actually the distinction between wave-like and non-wave-like behaviour can be fuzzy, as it is (in) the case of a solid sample excited by a periodic heat source. The resulting temperature oscillations inside the sample have the same mathematical expression as highly damped waves, the so-called thermal waves. The aim of this paper is to stress the energy propagation as the key to affirm whether there is wave motion. In this way it is demonstrated that there is no wave nature in these improperly called thermal waves by showing that they do not transport energy. This result has been obtained not only in the frame of the parabolic heat conduction equation that evidences the diffusive nature of the heat conduction process, but also in the frame of the hyperbolic heat conduction equation, that is a wave equation.
(http://iopscience.iop.org/0143-0807/27/6/009;jsessionid=7EEBE3DE11D1236639104C7F411A52DD.c1)

- which supports my disbelief in the wave nature of heat diffusion.

Good-oh. How are you with Excel? Did my effort arrive in workable form, and were you able to tinker with it?

It needs more work, but it might be a worthwhile excercise to arrive at something really simple which can be used to demonstrate how diffusivity works, and which is transparent so that the workings behind it can be seen. I find that is the trouble with the sort of thing Barney suggested - while it is good in that it gives you a result, it is frustrating that you can't see how it got there.

boffin = geek without hair (unless female it which case lots of hair).

If we ever come up with a simple, generally agreed explanation of thermal diffusivity please could you announce is on a new thread and I'll stop baffling myself with this one!

thank you

Robinb

You'll probably not want to grapple with this:-

http://galileo.phys.virginia.edu/classes/311/notes/dimension/node8.html

but (if it works) you might like this animation of heat diffusing along a rod:-

http://galileo.phys.virginia.edu/classes/311/notes/dimension/diffusion.avi

I wonder if it is really the same curve we're seeing, just squashed and stretched as time passes. Mathematician in the house?

Thanks to all who have sent stuff for me over the years, beyond my current ability to grasp - keep it coming. One day I will spend a fortnight searching GBF to catch up with all that I missed first time.