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

[Cornel]

Hello,

Mathcad Prime 8 file attached.

[-MFra-]

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.

[-MFra-]

In the MATHCAD15 help you will find this and more:

[-MFra-]

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

[-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.

[ValeryOchkov]

Differential Equations in Thermal Engineering | SpringerLink

[rgunwaldsen · Accepted solution]

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.