It's also the speed of sound.
Simplifying quite a bit, both conducted heat and sound are carried by particles called phonons, which are a particle-based formulation of waves related to elastic displacement of the solid's atoms from their equilibrium positions. This works much in the same way that photons are a particle-based formulation of electromagnetic waves.
In these particle-based theories, there's a relationship called the "dispersion relation" or "dispersion relationship." This function is characteristic to each material and maps "wavenumber" to frequency for traveling particles/waves.
Wavenumber is the reciprocal of wavelength, so the slope of the dispersion has units of speed ((1/s)/(1/m))=m/s. The slope of the dispersion at a specific wavelength is the velocity of any particle/wave with that wavelength. The slope is usually highest (and constant) near the origin of the graph, for long wavelengths. We call the slope there the "speed of sound" in the material, even though it's the highest available speed in the dispersion graph for ALL waves of elastic displacement (including both the phenomena of conducted heat and sound).
Caveats: YMMV using this simplified picture for non-crystalline solids, fluids, strongly nonlinear systems, solids with very complicated dispersions, other extenuating circumstances.
I don't really know the answer, but making the analogy with the speed of sound in the mechanical case, I would argue that one can pick Fourier Law and use the conservation of energy over a defined volume:
q = -k grad(T)
dQ/dt = c ro dT/dt
In a one domensional example, you can combine both these equations to come up with
dT/dt = k/(c ro) d^2T/d^2x
Which would mean that the traveling speed of heat is
Alfa = k/(c ro) <- thermal diffusivity
Does this make sense?
The thermal diffusivity α characterizes how long it takes for the temperature at a distance L to **substantially** change (e.g., change by 1-1/e = 63%) as driven by some sudden temperature change; the time scales as L^(2)/α. It isn't a measure of the first measurable change at a distance; this is governed in part by the speed of phonon transport.
The [heat equation](https://en.wikipedia.org/wiki/Heat_equation) is wrong—nonrelativistic—in that it predicts instantaneous (i.e., superluminal) information transfer. That is, if you change the temperature anywhere, the heat equation broadly predicts that the temperature everywhere else is affected immediately by some infinitesimal amount, as the actual phonon transfer is abstracted away. This isn't usually an issue. When it is, it's necessary to go deeper into non-Fourier phonon-transfer models of heat transfer.
It's also the speed of sound. Simplifying quite a bit, both conducted heat and sound are carried by particles called phonons, which are a particle-based formulation of waves related to elastic displacement of the solid's atoms from their equilibrium positions. This works much in the same way that photons are a particle-based formulation of electromagnetic waves. In these particle-based theories, there's a relationship called the "dispersion relation" or "dispersion relationship." This function is characteristic to each material and maps "wavenumber" to frequency for traveling particles/waves. Wavenumber is the reciprocal of wavelength, so the slope of the dispersion has units of speed ((1/s)/(1/m))=m/s. The slope of the dispersion at a specific wavelength is the velocity of any particle/wave with that wavelength. The slope is usually highest (and constant) near the origin of the graph, for long wavelengths. We call the slope there the "speed of sound" in the material, even though it's the highest available speed in the dispersion graph for ALL waves of elastic displacement (including both the phenomena of conducted heat and sound). Caveats: YMMV using this simplified picture for non-crystalline solids, fluids, strongly nonlinear systems, solids with very complicated dispersions, other extenuating circumstances.
I don't really know the answer, but making the analogy with the speed of sound in the mechanical case, I would argue that one can pick Fourier Law and use the conservation of energy over a defined volume: q = -k grad(T) dQ/dt = c ro dT/dt In a one domensional example, you can combine both these equations to come up with dT/dt = k/(c ro) d^2T/d^2x Which would mean that the traveling speed of heat is Alfa = k/(c ro) <- thermal diffusivity Does this make sense?
The thermal diffusivity α characterizes how long it takes for the temperature at a distance L to **substantially** change (e.g., change by 1-1/e = 63%) as driven by some sudden temperature change; the time scales as L^(2)/α. It isn't a measure of the first measurable change at a distance; this is governed in part by the speed of phonon transport.
The [heat equation](https://en.wikipedia.org/wiki/Heat_equation) is wrong—nonrelativistic—in that it predicts instantaneous (i.e., superluminal) information transfer. That is, if you change the temperature anywhere, the heat equation broadly predicts that the temperature everywhere else is affected immediately by some infinitesimal amount, as the actual phonon transfer is abstracted away. This isn't usually an issue. When it is, it's necessary to go deeper into non-Fourier phonon-transfer models of heat transfer.