An $8-$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 $0C.$ The tank is located in a room whose temperature is $25C.$ Heat transfer between the outer surface of the tank and the surroundings is by natural convection and radiation in parallel. The convection heat transfer coefficients at the inner and the outer surfaces of the tank are $80\frac{W}{m^2}*K$ and $10\frac{W}{m^2}*K,$ respectively, and you can model the $"h"$ of radiation to be $5\frac{W}{m^2}*K($i$.$e$.,$ pretending it's a second "convection"$).$ Determine $($a$)$ the rate of heat transfer to the iced water in the tank and $($b$)$ the amount of ice at $0C$ that melts during a $24-h$ period. The heat of fusion$/$melting of water at atmospheric pressure is $h_{if}=333\mathrm{.}7k\frac{J}{k}g.$

Answers: $63131$ W$,16346$ kg