$2.)($Horizontal and Vertical Plates$)$ Consider an electrical power transformer of diameter $230$ mm and height $500$ mm whose lateral surface is being maintained at $47C$ by a forced convection coolant line wrapped around the outside surface removing $1000$ W $.$ It is now desired to explore cooling of the transformer by free convection and radiation instead, assuming the surface to have an emissivity of $0\mathrm{.}80.$

a$.$ Determine how much power could be removed by free convection and radiation from the lateral and the upper horizontal surface when the ambient temperature and the surroundings are at $27C.$ There is no heat loss through the bottom. $($Note: The sidewall of the cylinder may be treated as a vertical plate. For the top surface, use Eq$.9\mathrm{.}30$ from your textbook, $\frac{?}{\text{b}\text{a}\text{r}}({)}_L=0\mathrm{.}54R{a}_L^{\frac{1}{4}}.$ The characteristic length in this case is defined as $($:$L_c=\frac{A_s}{P}.$