Thermodynamics HW Solutions 55

Thermodynamics HW Solutions 55 - 2 2 2 m 65 . 28 m) 02 . 3...

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Chapter 1 Basics of Heat Transfer 1-107 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 0 that melts during a 24-h period are to be determined. ° C 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 h if = 333 7 . kJ / kg. The emissivity of the outer surface of the tank is 0.6. Analysis (a) The outer surface area of the spherical tank is
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Unformatted text preview: 2 2 2 m 65 . 28 m) 02 . 3 ( = = = D A s Then the rates of heat transfer to the tank by convection and radiation become W 780 , 22 1292 488 , 21 W 1292 ] ) K 273 ( K) 288 )[( K . W/m 10 )(5.67 m 65 . 28 )( 6 . ( ) ( W 488 , 21 C ) 25 )( m C)(28.65 . W/m 30 ( ) ( rad conv total 4 4 4 2-8 2 4 4 rad 2 2 conv = + = + = = = = = = = Q Q Q T T A Q T T hA Q s surr s s s & & & & & 1 cm C Iced water C Q & Air 25 C (b) The amount of heat transfer during a 24-hour period is kJ 000 , 968 , 1 s) 3600 kJ/s)(24 78 . 22 ( = = = t Q Q & Then the amount of ice that melts during this period becomes kg 5898 = = = = kJ/kg 7 . 333 kJ 000 , 968 , 1 if if h Q m mh Q Discussion The amount of ice that melts can be reduced to a small fraction by insulating the tank. 1-55...
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