I am trying to solve the following heat equation ODE:
d^2T/dr^2+1/r*dT/dr=0 (steady state) or
dT/dt=d^2T/dr^2+1/r*dT/dr (transient state)
The problem is simple: a ring with r1<r<r2, T(r1)=T1, T(r2)=T2.
I have searched the analytical solution for this kind of ODEs in polar coordinate...
Thank you AlephZero. Your reply helps me a lot on understanding the problem itself. About Fourier number and Biot number, I heard them before and I definitely gonna check them out.
I tried different theta values in Crank-Nicholson method, e.g. U(t+dt)=U(t)+theta*dU
It turns out that with bigger...
I am a noob so please let me know if here isn't the right place to post this.
Recently I am trying to solve hyperbolic equation m*dU/dt=k*d^2U/dx^2+q using Crank-Nicholson and finite element method. The final form of the solution is to compute the increment of the unknown at each time step...