Question $1(30$ points$)$ : An ice skating rink is located in a building where the air is at $T_{\text{a}\text{i}\text{r}}=20C.$ The convection heat transfer coefficent between the ice and surrounding air is $h=10\frac{W}{m^2}K.$ The emissivity of ice is $=0\mathrm{.}95.$ The latent heat of fusion of ice is $h_{if}=333\mathrm{.}7k\frac{J}{k}g$ and its density is $920k\frac{g}{m^3}.$

a$.$ Calculate the refrigeration load of the system necessary to maintain the ice at $T_s=0C$ for an ice rink of $12$ m by $40$ m $.D_1,D_2$

b$.$ How long would it take to melt $3$ mm thick ice from the surface of the rink if no cooling is supplied and the surface is considered insulated on the back side?