Chapter 1, Problem 98P

A 3-m-internal-diameter spherical tank made of 1-cm-thick stainless steel is use to store iced water at $0^{\text{o}}\text{C}\text{.}$

The tank is located outdoors at ${25}^{\text{o}}\text{C}\text{.}$

Assuming the entire steel tank to be at $0^{\text{o}}\text{C}$ and thus the thermal resistance of the tank to be negligible, determine (a) the rate of heat transfer to the iced water in the tank and (b) the amount of ice at $0^{\text{o}}\text{C}$ that melts during a 24-h period. The heat of fusion of water at atmospheric pressure is $h_{if}=333.7\text{kJ/kg}.$ and The emissivity of the outer surface of the tank is 0.75, and the convection heat transfer coefficient on the outer surface can be taken to be ${\text{30 W/m}}^{\text{2}\text{.}}\text{K}\text{.}$

Assume the average surrounding surface temperature for radiation exchange to be ${15}^{\text{o}}\text{C}\text{.}$