$(20$ points$)$ A cylindrical nuclear fuel element is $11\mathrm{.}16$ cm long and $11\mathrm{.}77$ cm in diameter. The fuel generates heat uniformly at a constant rate $S_e=51\mathrm{.}7{10}^{3}k\frac{J}{s}*m^3.$ The fuel is placed in an environment having a temperature of $360$ K with a surface coefficient $h=4540\frac{W}{m^2}*K.$ The fuel material has $k=33\mathrm{.}9\frac{W}{m}*K.$ Determine the temperature profile as a function of radial position r$.($ID $-$ Steady State with constant heat generation$)$