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Forgotten my maths! Simple 1D ODE, spherical coordinates

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JHZR2
#1
Sep13-11, 09:35 PM
P: 2
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!
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tiny-tim
#2
Sep14-11, 03:27 AM
Sci Advisor
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tiny-tim's Avatar
P: 26,148
Hi JHZR2!
Quote Quote by JHZR2 View Post
0 = 1/r^2 ∂/∂r (D*r^2 ∂C/∂r) + P
(try using the X2 icon just above the Reply box )

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


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