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