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Second Fick's law with nonconstant diffusion coefficient

  1. Jan 13, 2015 #1
    Hello everybody.
    I should solve a modified version of second Fick's law in nondimensional spherical coordinates; t is the time and rho [0,1] the nondimensional radius. In this equation the diffusion coefficient is vraiable with t and rho.

    The equation is the following:

    dC/dt = (1/rho^2)*d/d(rho)(rho^2*D(rho,t)*dC/d(rho))

    Initial conditions:
    C(0,rho) = a*rho^4 + b*rho^2 -(a + b);

    Boundary conditions:
    dC(t,0)/d(rho) = 0
    C(t,1) = 0

    Is it possible to solve such an equation by Laplace transforms?
    Alternatively, is there a user friendly tool for numerical solution of a PDE like this?

    Thanks in advance, cheers.
    Marco
     
  2. jcsd
  3. Jan 13, 2015 #2
    I don't think an analytic solution exists. It would have to be solved numerically. I would just convert it to a set of ODE's using the method of lines, and then solve the equations numerically in FORTRAN using an automatic (stiff) integration package.

    Chet
     
  4. Jan 23, 2015 #3
    Thanks a lot for the suggestion, I really appreciate it. I'll try to develop a routine using MOL.
    Cheers,
    Marco
     
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