I need to solve:

$\displaystyle \nabla ^2 T = 0$ with T=T(r) and r=a/T=T1 and r=b/T=T2

Can anyone offer advice as to the solution?

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- Nov 19th 2009, 10:10 AMbigdoggylaplacian
I need to solve:

$\displaystyle \nabla ^2 T = 0$ 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, 03:36 PMJester
I'm assuming that you're only in 2D. Laplace's equation in polar coords is

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

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

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

which you can solve. Then impose your boundary conditions.