Problem $4(10pts)$: The tip of a soldering iron consists of a $0\mathrm{.}6-cm-$diameter copper rod, $7\mathrm{.}6$

cm long. Assume that $T_{\text{a}\text{i}\text{r}}=21C,$ and the thermal conductivity of copper is $388\frac{W}{m}K.$ The

convective heat transfer coefficient along the rod and at the tip of the rod can be taken as $h=$

$22\mathrm{.}7\frac{W}{m^2}K.$

a$.$ If the tip must be $204C,$ what are the required minimum temperature of the base and

the heat flow $($in watts$)$ into the base? Write down the boundary conditions and the

equation that you use to solve this problem. Note: You can refer to Equations $17-36$ to

$17-46$ in the textbook for the expressions for temperature profile and heat flow at the

specific boundary conditions. $(8$ pts $)$

b$.$ A typical soldering iron is rated for $30$ W $,$ which is much higher than the heat flow

required calculated in $($a$).$ Provide one reason why. $(2$ pts$)$