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Fick's Second Law: Laplace Transform to solve PDE in Spherical Coords

  1. Dec 9, 2008 #1
    Fick's second law in general form:
    [tex]\frac{\partial C}{\partial t} = D\nabla^2 C[/tex]

    In spherical form:
    [tex]\frac{\partial C}{\partial t} = D\frac{1}{r^2}\frac{\partial}{\partial r}\left( r^2\frac{\partial C}{\partial r} \right)[/tex]

    (Assume all changes in phi and theta to be zero, so we are only concerned with the r component here.)

    Let's say that C(t=0) = 0

    If we laplace transform:
    LHS becomes: [tex]p\bar{C}}[/tex]

    Where C bar is the laplace transform of C, and C(t=0) = 0.

    I'm stuck on the right hand side. The textbook just skips the math and gives the solution. Any help would be appreciated.

    Last edited: Dec 9, 2008
  2. jcsd
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