Science > Physics > Will this work for back-of-the-envelope thermal diffusion?
| Topic: |
Science > Physics |
| User: |
"Paul Ciszek" |
| Date: |
05 Jul 2006 03:27:15 PM |
| Object: |
Will this work for back-of-the-envelope thermal diffusion? |
I have been trying to get a handle on thermal diffusion from the links
posted here. I was wondering if the following approximation will work
for estimating the "speed" 1-dimensional heat dissapation in a solid:
t = d^2/alpha
where t is time, d is distance, and alpha is the thermal diffusivity
defined as alpha = (thermal conductivity)/(heat capacity per unit
volume)
In other words, if I start with a temperature "bump" in a strip of
material and wait t seconds, will I find that the half-maximum points
of the "bump" have spread outward by approximately d = SQRT(t/alpha)?
Or am I missing some constants here? I can do a detailed simulation
later, but I want to estimate what sort of time scale to expect for a
given distance.
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Please reply to: | "Any sufficiently advanced incompetence is
pciszek at panix dot com | indistinguishable from malice."
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| User: "Paul Ciszek" |
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| Title: Re: Will this work for back-of-the-envelope thermal diffusion? |
05 Jul 2006 03:29:03 PM |
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In article <e8h7b3$b3t$1@reader2.panix.com>,
Paul Ciszek <nospam@nospam.com> wrote:
In other words, if I start with a temperature "bump" in a strip of
material and wait t seconds, will I find that the half-maximum points
of the "bump" have spread outward by approximately d = SQRT(t/alpha)?
Whoops, make that SQRT(t*alpha). Alpha has dimensions of distance
squared over time.
--
Please reply to: | "Any sufficiently advanced incompetence is
pciszek at panix dot com | indistinguishable from malice."
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| User: "" |
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| Title: Re: Will this work for back-of-the-envelope thermal diffusion? |
05 Jul 2006 04:53:53 PM |
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In article <e8h7b3$b3t$1@reader2.panix.com>, (Paul Ciszek) writes:
I have been trying to get a handle on thermal diffusion from the links
posted here. I was wondering if the following approximation will work
for estimating the "speed" 1-dimensional heat dissapation in a solid:
t = d^2/alpha
where t is time, d is distance, and alpha is the thermal diffusivity
defined as alpha = (thermal conductivity)/(heat capacity per unit
volume)
Yes, for careful definitions of "speed".
In other words, if I start with a temperature "bump" in a strip of
material and wait t seconds, will I find that the half-maximum points
of the "bump" have spread outward by approximately d = SQRT(t/alpha)?
Or am I missing some constants here? I can do a detailed simulation
later, but I want to estimate what sort of time scale to expect for a
given distance.
You're doing fine and the constans are OK as far as I can see.
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
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