Thermodynamics HW Solutions 293

Thermodynamics HW Solutions 293 - becomes F 166 = = = = = =...

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Chapter 4 Transient Heat Conduction 4-15E A number of brass balls are to be quenched in a water bath at a specified rate. The temperature of the 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 brass balls are given to be k = 64.1 Btu/h.ft. ° F, ρ = 532 lbm/ft 3 , and C p = 0.092 Btu/lbm. ° F. Analysis ( a ) The characteristic length and the Biot number for the brass balls are 1 . 0 01820 . 0 ) F Btu/h.ft. 1 . 64 ( ) 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 s c π Brass 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 166 = = = = = = = = ) ( 120 250 120 ) ( ) ( s 00858 . h 9 . 30 ft) F)(0.02778 Btu/lbm. 092 . )( lbm/ft (532 F . Btu/h.ft 42 s) 120 )( s 00858 . ( 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 97 . 9 F ) 166 250 ( F) Btu/lbm. 092 . )( lbm 29 . 1 ( )] ( [ lbm 290 . 1 6 ft) 12 / 2 ( ) lbm/ft 532 ( 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 1196 = = = ) Btu 97 . 9 ( balls/min) 120 ( ball ball Q n Q total &amp; &amp; Therefore, heat must be removed from the water at a rate of 1196 Btu/min in order to keep its temperature constant at 120 . F 4-4...
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This note was uploaded on 01/19/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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