|MadSci Network: Physics|
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. For more information on Fourier's Law, check out: http://en.wikipedia.org/wiki/Heat_conduction For more information on Fourier Series, check out: http://mathworld.wolfram.com/FourierSeries.html 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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