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Math Help - Heat Equation On an Annulus

  1. #1
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    Heat Equation On an Annulus

    The following partial differential equation describes the radially symmetric temperature distribution in the annulus 0<a<r<b, with constant temperature prescribed at r=a and r=b:

     u_t = \frac{1}{r} (ru_r)_r
    a<r<b, t>0

    Boundary Conditions:
    u(a,t) = 0, u(b,t)=1

    Initial Condition:
    u(r,0) = f(r)

    Find the steady-state temperature distribution v(r) = \lim_{ t \to \infty} u(r,t)

    Please help...it's due tomorrow.
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  2. #2
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    Quote Originally Posted by Creebe View Post
    The following partial differential equation describes the radially symmetric temperature distribution in the annulus 0<a<r<b, with constant temperature prescribed at r=a and r=b:

     u_t = \frac{1}{r} (ru_r)_r
    a<r<b, t>0

    Boundary Conditions:
    u(a,t) = 0, u(b,t)=1

    Initial Condition:
    u(r,0) = f(r)

    Find the steady-state temperature distribution v(r) = \lim_{ t \to \infty} u(r,t)

    Please help...it's due tomorrow.
    Maybe it's a bit too late but steady state means [imath]\frac{\partial u}{\partial t}=0[/imath] therefore you have an ordinary DE to solve which is fairly simple:

    \frac{d}{dr}\left(r\frac{du}{dr}\right)=0

    Can you take it from here?

    Coomast
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