I'm not sure on how to integrate this equation twice.
$$ \frac{1}{r} \frac{\partial}{\partial r} \left( \frac{r \partial T}{\partial r} \right) + \frac{e}{k} = 0 $$
After integrating twice the outcome is: $$ T(r) = -\frac{e}{4k} r^{2} + c_{1} \ln r + c_{2} $$
Where $c_{1}$ and $c_{2}$ are constants. After integrating it once it will give the rate of conduction heat transfer.
Thank you