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Math Help - laplacian

  1. #1
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    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?
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  2. #2
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    Quote Originally Posted by bigdoggy View Post
    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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