Forgotten my maths! Simple 1D ODE, spherical coordinates

  1. Hi,

    I seem to have forgotten some of my math how-to, as I havent done this in a while. Looking through my notes, Bird, Stewart and Lightfoot, Greenberg, etc. dont really help.

    My equation is this, at steady state:

    0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P

    Where P is some production rate.

    So the thing that I'm just not remembering is how to deal with the basic function:

    ∂/∂r (r^2 ∂C/∂r) in terms of how to deal with it to make it solvable.

    I was kind of under the impression that I should do a chain rule to make it a real ODE, which gives me:

    0 = D*( ∂2C/∂r2 + 2/r ∂C/∂r) + P

    Problem is that the 2/r would integrate into log(r). Implementing the BC for the sphere that at r=0, ∂C/∂r=0, I would have an undefined answer since I'd have Log(0).

    So something is wrong.

    Ive tried searching around, but most places just glaze over the operation to solve this. I dont think it is that hard, but my brain is empty on this at this point - Ive forgotten how.

    Can anyone advise and/or point me in the right direction?

    Thanks very much!
  2. jcsd
  3. tiny-tim

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    Hi JHZR2! :smile:
    (try using the X2 icon just above the Reply box :wink:)

    Rewrite it as ∂/∂r (D*r2 ∂C/∂r) = -Pr2, and integrate. :wink:
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