# laplacian

• Nov 19th 2009, 11:10 AM
bigdoggy
laplacian
I need to solve:
$\nabla ^2 T = 0$ with T=T(r) and r=a/T=T1 and r=b/T=T2

Can anyone offer advice as to the solution?
• Nov 19th 2009, 04:36 PM
Jester
Quote:

Originally Posted by bigdoggy
I need to solve:
$\nabla ^2 T = 0$ with T=T(r) and r=a/T=T1 and r=b/T=T2

Can anyone offer advice as to the solution?

I'm assuming that you're only in 2D. Laplace's equation in polar coords is

$T_{rr} + \frac{1}{r} T_r + \frac{1}{r^2} T_{\theta \theta} = 0.$

Asumming that $T = T(r)$ reduces this PDE to the ODE

$T_{rr} + \frac{1}{r} T_r = 0$

which you can solve. Then impose your boundary conditions.