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One-dimensional steady state conduction in Cylindrical coordinates

  1. Dec 4, 2016 #1
    Hello,
    Im having some issues with my task.

    1. The problem statement, all variables and given/known data

    The heat generation rate of a cylindrical fuel (D=0.2 m and 1 m long) is 160 kW.
    The thermal conductivity of the fuel is 100 W/mK and its surface temperature is
    maintained at 283 K. Determine the temperature at the axis.

    2. Relevant equations
    I tried to use this equation: 0=(1/r)*(d/dr)*(r*dT/dr)+q/k and Ive added the volume to it
    --> 0=(1/r)*(d/dr)*(r*dT/dr)+q/(k*V)


    3. The attempt at a solution
    im getting this at the end: T(r)=-1/4*q/(kV)*r2 + c1*ln(r) + c2
    i wanted to use the boundary condition that for r=0 ---> T=283K, but i cant type ln(0) into my calculator.
    I dont know how to go on.


    Best regards
     
  2. jcsd
  3. Dec 4, 2016 #2

    Henryk

    User Avatar
    Gold Member

    Temperature has to be finite everywhere. Therefore c1 = 0
     
  4. Dec 4, 2016 #3
    ok thank you very much. i understand why the temperature has to be everywhere finite, but why does it make c1=0? how is the relation to that?
    best regards
     
  5. Dec 4, 2016 #4

    Henryk

    User Avatar
    Gold Member

    because ln(r) diverges at r = 0, that's you have to reject this solution, i.e. set c1 to zero. It does satisfy the differential equation but it is not physical. It is actually very common practice in physics to reject solutions that satisfy mathematics but are not physically correct
     
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