A 3-m-internal-diameter spherical tank made of 1-cm-thick stainless steel is used to store iced water at 0°C. The tank is located outdoors at 25°C. Assuming the entire steel tank to be at 0°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°C that melts during a 24-h period. The heat of fusion of water at atmospheric pressure is hif? = 333.7?kJ/kg. 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 30?W/m2•K. Assume the average surrounding surface temperature for radiation exchange to be 15°C.
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A spherical tank located outdoors is used to store iced water at 0*C. The rate of heat transfer to the iced water in the tank and the amount of ice at that melts during a 24-h period are to be determined.
Assumptions 1 Steady operating conditions exist since the surface temperatures of the wall remain constant at the specified values. 2 Thermal properties of the tank and the convection heat transfer coefficient is constant and uniform. 3 The average surrounding surface temperature for radiation exchange is 15*C. 4 The thermal resistance of the tank is negligible, and the entire steel tank is at 0*C.
Properties The heat of fusion of water at atmospheric pressure is 
The emissivity of the outer surface of the tank is 0.75.
Analysis (a) The outer surface area of the spherical tank is
Then the rates of heat transfer to the tank by convection and radiation become
(b) The amount of heat transfer during a 24-hour period is
Then the amount of ice that melts during this period becomes
Discussion The amount of ice that melts can be reduced to a small fraction by insulating the tank.
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