Thermodynamics HW Solutions 376

Thermodynamics HW Solutions 376 - min 5 . m/min 10 m 5...

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Chapter 4 Transient Heat Conduction 4-109 A long roll of large 1-Mn manganese steel plate is to be quenched in an oil bath at a specified rate. The temperature of the sheet metal after quenching and the rate at which heat needs to be removed from the oil in order to keep its temperature constant are to be determined. Assumptions 1 The thermal properties of the balls are constant. 2 The heat transfer coefficient is constant and uniform over the entire surface. 3 The Biot number is Bi < 0.1 so that the lumped system analysis is applicable (this assumption will be checked). Properties The properties of the steel plate are given to be k = 60.5 W/m. ° C, ρ = 7854 kg/m 3 , and C p = 434 J/kg. ° C (Table A-3). Analysis The characteristic length of the steel plate and the Biot number are 1 . 0 036 . 0 C W/m. 5 . 60 ) m 0025 . 0 )( C . W/m 860 ( m 0025 . 0 2 < = ° ° = = = = = k hL Bi L A V L c s c Steel plate 10 m/min Oil bath 45 ° C Since , the lumped system analysis is applicable. Therefore, Bi < 0.1 s 30
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Unformatted text preview: min 5 . m/min 10 m 5 velocity length time s 10092 . m) C)(0.0025 J/kg. 434 )( kg/m (7854 C . W/m 860 1-3 2 = = = = = = = = c p p s L C h V C hA b Then the temperature of the sheet metal when it leaves the oil bath is determined to be C 82.53 = = = ) ( 45 820 45 ) ( ) ( s) 30 )( s 10092 . (-1 t T e t T e T T T t T bt i The mass flow rate of the sheet metal through the oil bath is kg/min 4 . 785 m/min) 10 ( m) 005 . ( m) 2 )( kg/m 7854 ( 3 = = = = wtV V m &amp; &amp; Then the rate of heat transfer from the sheet metal to the oil bath and thus the rate at which heat needs to be removed from the oil in order to keep its temperature constant at 45 C becomes kW 213.2 = J/min 10 279 . 1 C ) 45 53 . 82 )( C J/kg. 434 )( kg/min 4 . 785 ( ] ) ( [ 7 = = = T t T C m Q p &amp; &amp; 4-87...
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