laplacian

**bigdoggy** · November 19th 2009, 10:10 AM

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?

**Danny** · November 19th 2009, 03:36 PM

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.

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