Diffusion PDE solve

  • Thread starter wenzhe2092
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  • #1

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Dear all,

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

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

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.
 

Answers and Replies

  • #2
Dear all,

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.

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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