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P: 25
 Quote by coomast 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:
$$\frac{-g(r,z)}{k} = \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2}$$

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:
$$\frac{u_0}{k} = \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial r}+\frac{\partial^2 u}{\partial z^2}$$

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"