# DSolve: how to plot the heat equation solution?

Posted 9 years ago
4522 Views
|
2 Replies
|
0 Total Likes
|
 Hi everyoneFirst 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 complexThen 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
Sort By:
Posted 9 years ago
 Thank you very much for these explanations :)
Posted 9 years ago
 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}]