Thermodynamics HW Solutions 294

Thermodynamics HW Solutions 294 - becomes F 152 = = = = = =...

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Chapter 4 Transient Heat Conduction 4-16E A number of aluminum balls are to be quenched in a water bath at a specified rate. The temperature of balls after quenching and the rate at which heat needs to be removed from the water in order to keep its temperature constant are to be determined. Assumptions 1 The balls are spherical in shape with a radius of r 0 = 1 in. 2 The thermal properties of the balls are constant. 3 The heat transfer coefficient is constant and uniform over the entire surface. 4 The Biot number is Bi < 0.1 so that the lumped system analysis is applicable (this assumption will be verified). Properties The thermal conductivity, density, and specific heat of the aluminum balls are k = 137 Btu/h.ft. ° F, ρ = 168 lbm/ft 3 , and C p = 0.216 Btu/lbm. ° F (Table A-3E). Analysis ( a ) The characteristic length and the Biot number for the aluminum balls are 1 . 0 00852 . 0 ) F Btu/h.ft. 137 ( ) ft 02778 . 0 )( F . Btu/h.ft 42 ( ft 02778 . 0 6 ft 12 / 2 6 6 / 2 2 3 < = ° ° = = = = = = = k hL Bi D D D A V L c c π Aluminum balls, 250 ° F Water bath, 120 ° F The lumped system analysis is applicable since Bi < 0.1. Then the temperature of the balls after quenching
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Unformatted text preview: becomes F 152 = = = = = = = = ) ( 120 250 120 ) ( ) ( s 01157 . h 66 . 41 ft) F)(0.02778 Btu/lbm. 216 . )( lbm/ft (168 F . Btu/h.ft 42 s) 120 )( s 01157 . ( 1-1-3 2-1 t T e t T e T T T t T L C h V C hA b bt i c p p s ( b ) The total amount of heat transfer from a ball during a 2-minute period is Btu 62 . 8 F ) 152 250 ( F) Btu/lbm. 216 . )( lbm 4072 . ( )] ( [ lbm 4072 . 6 ft) 12 / 2 ( ) lbm/ft 168 ( 6 3 3 3 = = = = = = = t T T mC Q D V m i p Then the rate of heat transfer from the balls to the water becomes Btu/min 1034 = = = ) Btu 62 . 8 ( balls/min) 120 ( ball ball Q n Q total &amp; &amp; Therefore, heat must be removed from the water at a rate of 1034 Btu/min in order to keep its temperature constant at 120 . F 4-5...
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