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DSolve: how to plot the heat equation solution?

Posted 10 years ago

Hi everyone

First of all, sorry for my poor english, that's not my native language.

Secondly I'm trying to solve the heat equation with spherical coordinates but I have some issues in plotting the solution. Here's my problem: I'm solving the heat equation with a spherical laplacian and I'm considering that the temperature only depends on the radius r. There are two sources of temperature: one at T1 at r=rmin et an other one at T2 at r=rmax. I'm solving the heat equation with a solution of the form T=T(r)e^(iwt) , where T(r) can be complex

Then the heat equation D*Laplacien(T)=d(T)/dt becomes DLaplacien(T(r))=iw*T(r)

Thus I wrote the following code:

 Thermalconductivity = 148
Thermalcapacity = 711
Density = 2338
d = N[Thermalconductivity/(Density*Thermalcapacity)]

f = 1
w = 2 Pi*f

T0 = 300
T1 = 300.1

rmin = 1.35*0.000001
rmax = 500*0.000001

r =. ..
sol = DSolve[{d T''[r] + (2 d/r) T'[r] == I w T[r], T[rmin] == T1, 
   T[rmax] == T0}, T[r], {r, rmin, rmax}]

Then I want to plot the modul of T, so I wrote:

Plot[Evaluate[Abs[T[r]]], {r, rmin, rmax}]

However I only got the two axes y;x without any curve -_-

Does anybody has an idea of where my mistake is?

Cheers

2 Replies

Thank you very much for these explanations :)

Dsolve returns a rule. See this article for information on how to use rules in this situation:

http://support.wolfram.com/kb/12505

Plot[Evaluate[Abs[T[r]]] /. First[sol], {r, rmin, rmax}]
POSTED BY: Sean Clarke
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