One-dimensional steady state conduction in Cylindrical coordinates

[Hannibal247]

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 I've 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 can't type ln(0) into my calculator.
I don't know how to go on. Best regards

 

[Henryk]

Temperature has to be finite everywhere. Therefore c₁ = 0

 

[Hannibal247]

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

 

[Henryk]

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