One-dimensional steady state conduction in Cylindrical coordinates

  • #1
Hello,
Im having some issues with my task.

1. Homework Statement

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.

Homework 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)[/B]

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
 

Answers and Replies

  • #2
Henryk
Gold Member
252
98
Temperature has to be finite everywhere. Therefore c1 = 0
 
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  • #3
Temperature has to be finite everywhere. Therefore c1 = 0
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
 
  • #4
Henryk
Gold Member
252
98
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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