Forgotten my maths! Simple 1D ODE, spherical coordinatesby JHZR2 Tags: coordinates, forgotten, maths, simple, spherical 

#1
Sep1311, 09:35 PM

P: 2

Hi,
I seem to have forgotten some of my math howto, 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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