Skip to main content
rgunwaldsenAnswer
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.

View in thread

6 replies

-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

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

In the MATHCAD15 help you will find this and more:

risposta a CornelBejan.jpg

Translate
-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

Translate
-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

 

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

Differential Equations in Thermal Engineering | SpringerLink

Translate
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.

Translate
    Terms & ConditionsAccessibility statement