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Solution of the 1D heat equation in cylindrical co-ordinates

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Old   March 25, 2022, 05:14
Default Solution of the 1D heat equation in cylindrical co-ordinates
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I am trying to solve the transient heat equation in cylindrical co-ordinates using finite differences and the Crank-Nicholson method. The problem I am having is that I cannot seem to get the inner boundary condition, which is the usual no-flux condition to work in my code. The heat drops at both the centre and the outer edge, this is clearly unphysical but I don't know what's going on. I tried the same method to solve the spherical case and it worked perfectly. Can someone tell me what I'm doing wrong or is it simply not possible to solve the heat equation in cylindrical co-ordinates using finite differences?

I have attached my derivation of the method.
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File Type: pdf cylindrical_heat.pdf (173.4 KB, 33 views)
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