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Best answer by rgunwaldsen

Perhaps this may be a help. I dusted off some very old notes and slogged through a solution to your posed problem using only the standard/usual Prime 8 functions.

 

Then I used the numol() function found in Prime 8. Much easier! But, of course, numol() returns a matrix of time-spatial data points rather than an u(x,t) function.

5 replies

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-MFra-21-Topaz II
21-Topaz II
April 15, 2023

f(x) is missing. The system has cylindrical symmetry. The equation is partial differential. You have to apply Pdesolve(). But you should first and at the very least study the examples provided in the help. Without PRIME 9, being the problem an initial values one, you have to discretize all the linear operators, replace them in the starting equation, simplify, and first of all you have to see if it converges and is stable, otherwise you have to change the approximations with more suitable ones.

IVP 0.jpgIVP 1.jpgIVP 2.jpgIVP 3.jpgIVP 4.jpg

IVP 5.jpgIVP 6.jpg

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-MFra-21-Topaz II
21-Topaz II
April 17, 2023

In the MATHCAD15 help you will find this and more:

risposta a CornelBejan.jpg

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-MFra-21-Topaz II
21-Topaz II
April 17, 2023

Analysis in one dimension is simple. Also in the case of cylindrical symmetry the final system can be solved with odesolve.

risposta a CornelBejan 1.jpg

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-MFra-21-Topaz II
21-Topaz II
April 18, 2023

It is evident that in the last part I have not considered W(z). Also considering W(z), the problem becomes somewhat more complicated.

non omogenea.jpg

 

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
April 18, 2023

Differential Equations in Thermal Engineering | SpringerLink

R
rgunwaldsen15-MoonstoneAnswer
15-Moonstone
April 18, 2023

Perhaps this may be a help. I dusted off some very old notes and slogged through a solution to your posed problem using only the standard/usual Prime 8 functions.

 

Then I used the numol() function found in Prime 8. Much easier! But, of course, numol() returns a matrix of time-spatial data points rather than an u(x,t) function.

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