Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.
  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.

  4. Jan 23, 2015 #3
    Thanks a lot for the suggestion, I really appreciate it. I'll try to develop a routine using MOL.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Similar Threads for Second Fick's nonconstant
Thermodynamic second derivatives?