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phioder
phioder is offline
#21
Feb3-08, 11:56 AM
P: 25
Quote Quote by coomast View Post
Hope this helps you one step further.
Hello coomast

Thank you very much for your answer. You make special comments that make me further understand small details I haven't understand yet.

After doing some research, as much as I understand now, the problem is indeed complicated and not trivial. During all this thread I have tried to split the problem and state basic questions because my knowledge and experience in PDE is very limited.

To reduce the complexity splitting the problem was based on:
1.- 2D steady heat conduction, no transients, no time dependency, no phi dependency, dependencies only on r and z
2.- For a first try the heat source considered as uniform
3.- For a first try not von Neumann boundary conditions, the heat needs to enter the cylinder from the upper part, all other sides are insulated

The equation is following:
[tex]\frac{-g(r,z)}{k} =
\frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot
\frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2} [/tex]

From this link http://www.engr.unl.edu/~glibrary/gl...05b/node4.html what I understand is that the function g(r,z) is the heat source. They give a solution with green functions, unfortunately I don't understand them to implement a program.

If the heat souce is constant the equation is following:
[tex]\frac{u_0}{k} =
\frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot
\frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2} [/tex]

Unfortunately I began to loose focus and my post can't be well formulated, my apologies

Best Regards
phioder

PS: What does it mean that a solution is "bounded" or "not bounded"