First multiply through by to get . That's Bessel's equation of order 0. Look up "Bessel's function".
I'm trying to solve the diffusion PDE for my system, shown below:
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.
One of the ODE is:
where lamba is a constant.
Does any one have any ideas on how to solve this ODE tro obtain a general solution? I tried using a change in variables.
Any help would be appreciated. Thanks in advance!
Well, I can't give an entire course on Bessel's equation. Doesn't your text book deal with it? Here is a link to the Wikipedia article:
Bessel function - Wikipedia, the free encyclopedia
Typically, you determine what values the eigenvalue can take by looking at the boundary conditions.
So far i have established my principal solution for my ODE, as shown below:
Now to solve it. The initial condition is given as c(r,0) = 0.0398 mol/m^3 for a<r<b where a and b are the inner and outer radius respectively.
Any tips on how to apply this condition?
Next, the boundary condition is such that:
c= o at r = b
c= 0.433 at r = a
Any help appreciated! Thanks.