Speed of heat conduction through glass

simple_logic

Is anyone here familiar with the speed of a temperature wave through Si02 or other electrical insulators?

Thanks,

S.L.

Bill_K

simple_logic, Why are you asking this on the Relativity forum?? The Solid State forum would be a much more logical place.

Anyway, temperature does not propagate as a wave, it diffuses, so there is no speed associated with it. The relevant parameter is thermal conductivity.

simple_logic

http://en.wikipedia.org/wiki/Relativ...eat_conduction

simple_logic

Bill, you are correct, the question should be rephrased as:

Is anyone here familiar with the speed of temperature diffusion through Si02 or other electrical insulators?

Bill_K

Ok, now we are on the same page. The Wikipedia article talks about two models, the HHC (Telegraph Equation) and the RHC, in which heat conduction is made out to be Lorentz invariant. It labels these theories "controversial" and describes objections to them. I have some comments.

Thermal energy in a nonconducting solid resides in the lattice vibrations or phonons. If these are given a chance to come to thermal equilibrium through phonon-phonon collisions, the solid has a well-defined temperature T. In non-equilibrium thermodynamics one further considers situations in which, although the temperature is well-defined everywhere, it is a slowly varying function of position. A consequence of this is that T obeys the Heat Equation, a diffusion equation with a diffusion constant (thermal conductivity) that can be calculated from properties of the solid. The equation is parabolic, meaning there is no upper limit to the speed at which influences propagate. This is in apparent conflict with relativity.

My opinion is that the RHC is an extremely naive attempt to reconcile this, and gives insufficient consideration to the approximations that went into deriving the Heat Equation in the first place. At the "leading edge" of a heat pulse, the number of phonons becomes exponentially small, too small to support the thermodynamic approximation. Consequently there is no well-defined temperature in this limit, invalidating the idea that T exists and obeys some relativistic equation.

simple_logic

Is anyone here is familiar with the speed of temperature diffusion through any electrical insulators?

For those unfamiliar with the subject, Heat propagates at relativistic speeds<sup>1

1</sup>: Ali, Y., and L. Zhang. "Relativistic Heat Conduction." International Journal of Heat and Mass Transfer 48.12 (2005): 2397-406

Chestermiller

I assume you are talking about transient heat conduction through a solid material. As Bill_K indicated this is a diffusional type process. The key physical property parameter is the thermal diffusivity, which is equal to the thermal conductivity divided by the product of heat capacity times density. The units of thermal diffusivity are m²/s, which are the same as the concentration diffusion coefficient in Fick's second law.

What happens is that a thermal boundary layer develops at the heated surface. Within the thermal boundary layer, the temperature varies very rapidly with spatial position. As time progresses, the thermal boundary layer grows in thickness, until it penetrates through to the far boundary of the solid. The boundary layer grows as "kind of" a wave, moving across the solid slab. The thickness of the boundary layer is roughly described by:

[itex]\delta[/itex] ~ sqrt ([itex]\alpha[/itex]t)

where [itex]\alpha[/itex] is the thermal diffusivity and t is the time. I hope this is helpful. If you want to learn more detail, get a book like Heat Transmission by McAdams or Transport Phenomena by Bird, Stewart, and Lightfoot.

Chet

Hypatio

Glasses have a low conductivity. I'm not sure the conductivity (can be figured out as k=DrC, where D is thermal diffusivity, r is density, and C is specific heat) but all silicate glasses seem to have a thermal diffusivity on the order of 0.5-0.6 mm2/s at standard PT.

See:
Hofmeister, Whittington, Pertermann, 2009, Transport properties of high albite crystals, near-endmember feldspar and pyroxene glasses, and their melts to high temperature, Contrib Mineral Petrol.

Branlund and Hofmeister, 2008, Factors affecting heat transfer in natural SiO2 solids, American Mineralogist, 93, 1620-1629.

marcusl

Did you even bother to read this article? It derives heat conduction in a relativistic framework and shows that conduction speeds are finite (and slow compared to the speed of light).