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Log transform on cylindrical coordinates

  1. Nov 4, 2012 #1
    1. The problem statement, all variables and given/known data
    I'd like to do a log transform on the radius variable of the heat conservation equation:

    qr - qr + Δr= ΔE/Δt

    where qr= -kA(dT/dr)

    My solution for this equation in cylindrical coordinates is:

    Tt+Δt=Tt+(Δt*k)/(ρ*c*Δr^2)* [(Tt-1-Tt)/(ln(rt/rt-1) - (Tt-Tt+1)/(ln(rt+1/rt)]

    3. The attempt at a solution

    I've written a matlab program with this transient eq. and I'd like to be able to have r be logarithmic so that there are a lot of radius nodes for small radii and less for more distant radii.

    dT/dlog(r) = r * dT/dr?

    qr = -k(A)r dT/dr?

    how can I log transform the transient eq for heat conservation? I've been struggling with this..
     
    Last edited: Nov 4, 2012
  2. jcsd
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