Thermodynamics HW Solutions 747

Thermodynamics HW Solutions 747 - 2 9 / 4 16 / 9 4 / 1 8 9...

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Chapter 9 Natural Convection 9-49 Water in a tank is to be heated by a spherical heater. The heating time is to be determined. Assumptions 1 Steady operating conditions exist. 2 The temperature of the outer surface of the sphere is constant. Properties Using the average temperature for water (15+45)/2=30 as the fluid temperature, the properties of water at the film temperature of ( T s + T )/2 = (85+30)/2 = 57.5 ° C are (Table A-9) Water T ,ave = 30 ° C Resistance heater T s = 85 ° C D = 6 cm D = 6 cm 1 - 3 2 6 K 10 501 . 0 12 . 3 Pr /s m 10 474 . 0 C W/m. 6515 . 0 × = = × = ° = β υ k Also, the properties of water at 30 ° C are (Table A-9) C J/kg. 4178 and kg/m 996 3 ° = = p C ρ Analysis The characteristic length in this case is L c = D = 0.06 m. Then, 8 2 2 6 3 -1 3 2 2 3 10 108 . 8 ) 12 . 3 ( ) /s m 10 474 . 0 ( ) m 06 . 0 )( K 30 85 )( K 10 501 . 0 )( m/s 81 . 9 ( Pr ) ( Ra × = × × = = D T T g s () [] () [] 14 . 89 12 . 3 / 469 . 0 1 ) 10 108 . 8 ( 589 . 0 2 Pr / 469 . 0 1 589 .
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Unformatted text preview: 2 9 / 4 16 / 9 4 / 1 8 9 / 4 16 / 9 4 / 1 = + + = + + = Ra Nu 2 2 2 2 m 01131 . m) 06 . ( C . W/m 9 . 967 ) 14 . 89 ( m 06 . C W/m. 6515 . = = = = = = D A Nu D k h s The rate of heat transfer by convection is W 1 . 602 ) 30 )(85 m C)(0.01131 . W/m 9 . 967 ( ) ( 2 2 conv = = = T T hA Q s s & The mass of water in the container is kg .84 39 ) m )(0.040 kg/m 996 ( 3 3 = = = V m The amount of heat transfer to the water is J 10 4.994 = C 15)-C)(45 J/kg. kg)(4178 84 . 39 ( ) ( 6 1 2 = = T T mC Q p Then the time the heater should be on becomes hours 2.304 = = = = s 8294 J/s 602.1 J 10 4.994 6 Q Q t & 9-48...
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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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