Problem #$2$

$4$ points

A $6-$m$-$internal$-$diameter spherical tank made of $1\mathrm{.}5$ cm thick stainless steel $(k=15\frac{W}{m}K)$ is used to store iced water at $0C$ in a room at $20C.$ The walls of the room are also at $20C.$ The outer surface of the tank is black and heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation. Assuming the entire steel tank to be at $0C$ and thus its thermal resistance to be negligible, determine:

A$)$ The total rate of heat transfer to the iced water in the tank $(2$ points$)$

B$)$ The amount of ice at $0C$ that melts during a $12$ hr period. The heat of fusion of water is $h_{if}=335k\frac{J}{k}g(2$ points$)$