### Re: What is the actual temperature profile of a bar heated at one end?

Date: Sun Aug 28 14:09:04 2005
Posted By: David Coit, Aerospace Engineer, Naval Air Warfare Center - Weapons Division
Area of science: Physics
ID: 1125016616.Ph
Message:
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Jim,

It's possible that you're confusing Fourier's Law with Fourier Series.
Fourier's Law is the governing law for conduction, while Fourier Series are
an infinite sum of sines and cosines that can be used to approximate any
periodic function.

If a bar starts at room temperature but is heated at one end, the
temperature along the length of the bar will only rise. It may be possible
to create a "wave-like" or "sinusoidal" temperature profile by alternately
heating and cooling one end, but typically we aren't interested in that
problem. The discussion of a bar heated (or cooled) at one or both ends is
popular because it closely approximates one-dimensional conduction (ie the
temperature of the bar is uniform at any given cross-section). The 1-D
problem is the simplest approximation of real conduction, and provides a
great opportunity to learn the basics of heat transfer while keeping the
math as simple as possible. If you're interested in heat transfer, this is
a great place to start. You can google "one dimensional conduction" for
some online resources or pick up an introductory book in heat transfer
(although you might want to be careful: even a basic text in heat transfer
is probably written for juniors or seniors in college).

I hope this helps, and if you have further questions about conduction or
heat transfer in general, I'd be glad to go into more detail, so just ask.

David Coit

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