Heat Dissipation in a Ring

 

In an effort to put some physics content on here, I give you heat dissipation in a ring.  It starts off with a non-uniform heat distribution, as indicated by the color gradient on the ring, and eventually the heat dissipates as it goes toward equilibrium.  I made this a while back while studying Fourier series, I believe.

Here’s the animation:

HeatRing3

And the code that generated it:

fourierheat

Looking at that mess of code I realize that the whole thing could just as easily be modeled with the temperature being a sine wave as a function of theta in polar coordinates with decreasing amplitude over time.  There was some reason for the specific way it was formulated here that had to do with Fourier analysis.  There were other scraps of code before this part in the Mathematica file that had finite series approximations. I’ll revisit it at some point and see if the reason was useful at all.

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