wenzhe2092
Mar1-10, 06:14 AM
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.
T = Aexp (-\lambda^2 D t)
where -\lambda^2 is the separation constant and A is the integration constant
R(r) = BJ_{0}(\lambda r) + CY_{0} (\lambda r)
Principle solution given by:
C(r,t) = Aexp (-\lambda^2 D t) [BJ_{0}(\lambda r) + CY_{0} (\lambda r)]
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.
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.
T = Aexp (-\lambda^2 D t)
where -\lambda^2 is the separation constant and A is the integration constant
R(r) = BJ_{0}(\lambda r) + CY_{0} (\lambda r)
Principle solution given by:
C(r,t) = Aexp (-\lambda^2 D t) [BJ_{0}(\lambda r) + CY_{0} (\lambda r)]
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.