$(20$ points$)$ To improve the air quality of your cabin, you would like to boil water atop a wood burning stove to increase the moisture content of the interior air. The process simply involves heating the water in a metal pan until enough water boils off. Assume nucleate boiling and model the water as a pool boiling of water at $101\mathrm{.}325$ kPa $.$

a$.$ What is the heat flux $\frac{W}{m^2}$ to the water?

b$.$ What is the convection heat transfer coefficient $\frac{W}{m^2}*(K)$ to the water?

c$.$ What is the water boil off rate $[$liters$/$hr$]?$

pan $($polished copper$)$

$T_s=380\mathrm{.}15K$

$A_{\text{p}\text{a}\text{n}}=650c{m}^2$