$2-114$ A circular metal pipe has a wall thickness of $10$ mm and an inner diameter of $10$ cm $.$ The pipe's outer surface is subjected to a uniform heat flux of $5k\frac{W}{m^2}$ and has a temperature of $500C.$ The metal pipe has a variable thermal conductivity given as $k(T)=k_n(1+T),$ where $k_0=7\mathrm{.}5\frac{W}{m}*K,=0\mathrm{.}0012K^{-1},$ and $T$ is in K $.$ Determine the inner surface temperature of the pipe.