A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convective heat transfer coefficient $1000 \: W/m^2-K$) at $25^{\circ}C$. At steady state, the surface temperature (in $K$) of the rod is
- $308$
- $398$
- $418$
- $448$