$(3)$ A $2-$kW resistance heater wire diameter $=4mm,$ length $=1\mathrm{.}2m$ with thermal conductivity

of $k=10\frac{W}{m}*C$ is used to boil water. If the outer surface temperature of the resistance wire

is $T_s=110C$ and the heat generation is uniform throughout the entire wire, determine the

temperature at the center of the wire $T_0.$ Hint: $q_{\text{g}\text{e}\text{n}}^{}=\frac{2000(W)}{r_0^{2}L}.,T_0=T_s+\frac{q_{\text{g}\text{e}\text{n}}^{}{r}_0^2}{4k}.,$ State

your assumptions, if any.

Start your answer for part $(3)$ here.