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How to solve 1D Heat Equation in Mathcad Prime 8?

Cornel
19-Tanzanite

How to solve 1D Heat Equation in Mathcad Prime 8?

Hello,

 

CornelBejan_0-1681497710734.png

CornelBejan_1-1681497730482.png

 

Mathcad Prime 8 file attached.

 

 

ACCEPTED SOLUTION

Accepted Solutions
rgunwaldsen
15-Moonstone
(To:Cornel)

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 solution in original post

6 REPLIES 6
-MFra-
21-Topaz II
(To:Cornel)

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

-MFra-
21-Topaz II
(To:Cornel)

In the MATHCAD15 help you will find this and more:

risposta a CornelBejan.jpg

-MFra-
21-Topaz II
(To:Cornel)

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

-MFra-
21-Topaz II
(To:-MFra-)

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

 

rgunwaldsen
15-Moonstone
(To:Cornel)

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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