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Diffusion PDE solve

  1. Mar 1, 2010 #1
    Dear all,

    I'm trying to solve the diffusion PDE for my system, shown below:

    \frac{\partial C}{\partial t} = D (\frac{\partial^2 C}{\partial r^2} + \frac{1}{r} \frac{\partial C}{\partial r})

    where C is the concentration, changing with time t and radius r. D is the diffusion coefficient.

    I'm solving this using seperation of variables, giving me two ODE.

    [tex] T = Aexp (-\lambda^2 D t) [/tex]

    where [tex]-\lambda^2 [/tex] is the separation constant and A is the integration constant

    [tex] R(r) = BJ_{0}(\lambda r) + CY_{0} (\lambda r) [/tex]

    Principle solution given by:

    [tex] C(r,t) = Aexp (-\lambda^2 D t) [BJ_{0}(\lambda r) + CY_{0} (\lambda r)] [/tex]

    My question is, given the boundary conditions and initial conditions of:

    C(0.0135,t) = 0.433
    C(0.0185,t) = 0
    C(r,0) = 0.0398

    How would i be able to solve this? I'm really stuck and any help would be appreciated. Note my system is a hollow cylinder.
  2. jcsd
  3. Mar 10, 2010 #2

    Look like the four unknowns A, B, C and [itex]\lambda[/itex] can just be reduced to three unknown. You only have three boundary and initial conditions.:wink:
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