$(15$ Points$)$ Water enters a thin$-$walled smooth circular metallic tube of diameter, $D=0\mathrm{.}01m,$ and length, $L=1m,$ at an average velocity and temperature of $u_m=0\mathrm{.}005\frac{m}{s}$ and $T_{mi}=95C,$ respectively. The air flowing outside the tube results in uniform external convection conditions corresponding to $h_o=100\frac{W}{m^2}K$ and $T_{}=20C.$ First, determine if you can use equations relevant for thermally fully developed flow inside the tube. Justify with appropriate calculations. Then, assuming fully developed flow in the tube, determine the average temperature of the water exiting the tube. Use the following as properties of water: $=983\mathrm{.}1k\frac{g}{m^3},=4\mathrm{.}68{10}^{-4}Pa.$s$,Pr=3,k=0\mathrm{.}6535\frac{W}{m}K,c_p=4189\frac{J}{k}gK,$ and $=\frac{0\mathrm{.}00051}{K}.$