Thermodynamics HW Solutions 765

Thermodynamics HW Solutions 765 - = = = ° = ° = = ππ o...

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Chapter 9 Natural Convection 9-97 A spherical tank made of stainless steel is used to store iced water. The rate of heat transfer to the iced water and the amount of ice that melts during a 24-h period are to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Thermal resistance of the tank is negligible. 4 The local atmospheric pressure is 1 atm. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (0+20)/2 = 10 ° C are (Table A-15) 1.5 cm Iced water D i = 6 m 0 ° C Q T s = 0 ° C T = 20 ° C 1 - 2 5 K 003534 . 0 K ) 273 10 ( 1 1 7336 . 0 Pr /s m 10 426 . 1 C W/m. 02439 . 0 = + = = = × = ° = f T k β υ Analysis ( a ) The characteristic length in this case is L c = D o = 6.03 m. Then, 11 2 2 5 3 -1 2 2 3 10 485 . 5 ) 7336 . 0 ( ) /s m 10 426 . 1 ( ) m 03 . 6 )( K 0 20 )( K 003534 . 0 )( m/s 81 . 9 ( Pr ) ( × = × = = o s D T T g Ra () [] () [] 5 . 394 7336 . 0 / 469 . 0 1 ) 10 485 . 5 ( 589 . 0 2 Pr / 469 . 0 1 589 . 0 2 9 / 4 16 / 9 4 / 1 11 9 / 4 16 / 9 4 / 1 = + × + = + + = Ra Nu 2 2 2 2 m 2 . 114 m) 03 . 6 ( C . W/m 596 . 1 ) 5 . 394 ( m 03 . 6 C W/m. 02439
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Unformatted text preview: . = = = ° = ° = = ππ o s o D A Nu D k h and W 3646 C ) 20 )( m 2 . 114 )( C . W/m 596 . 1 ( ) ( 2 2 = ° − ° = − = ∞ s s T T hA Q & Heat transfer by radiation and the total rate of heat transfer are kW 15.4 ≅ = + = = + − + × = − = − W 404 , 15 759 , 11 3646 W 759 , 11 ] ) K 273 ( ) K 273 20 )[( .K W/m 10 67 . 5 )( m 2 . 114 )( 1 ( ) ( 4 4 4 2 8 2 4 4 total surr s s rad Q T T A Q & & σε ( b ) The total amount of heat transfer during a 24-hour period is kJ/day 10 331 . 1 ) s/h 3600 h/day 24 )( kJ/s 4 . 15 ( 6 × = × = Δ = t Q Q & Then the amount of ice that melts during this period becomes kg 3988 = × = = ⎯→ ⎯ = kJ/kg 7 . 333 kJ 10 331 . 1 6 if if h Q m mh Q 9-88...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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