Thermodynamics HW Solutions 391

Thermodynamics HW Solutions 391 - Bi < 0.1, s...

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Chapter 4 Transient Heat Conduction 4-122 Long aluminum wires are extruded and exposed to atmospheric air. The time it will take for the wire to cool, the distance the wire travels, and the rate of heat transfer from the wire are to be determined. Assumptions 1 Heat conduction in the wires is one-dimensional in the radial direction. 2 The thermal properties of the aluminum 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 properties of aluminum are given to be k = 236 W/m. ° C, ρ = 2702 kg/m 3 , C p = 0.896 kJ/kg. ° C, and α = 9.75 × 10 -5 m 2 /s. Analysis ( a ) The characteristic length of the wire and the Biot number are 350 ° C 10 m/min Air 30 ° C Aluminum wire 1 . 0 00011 . 0 C W/m. 236 ) m 00075 . 0 )( C . W/m 35 ( m 00075 . 0 2 m 0015 . 0 2 2 2 2 < = ° ° = = = = = = = k hL Bi r L r L r A V L c o o o s c π Since the lumped system analysis is applicable. Then,
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Unformatted text preview: Bi &lt; 0.1, s 144 = = = = = = = t e e T T T t T L C h V C hA b t bt i c p p s ) s 0193 . ( 1-3 2-1 30 350 30 50 ) ( s 0193 . m) C)(0.00075 J/kg. 896 )( kg/m (2702 C . W/m 35 ( b ) The wire travels a distance of m 24 = = = s) m/s)(144 60 / 10 ( length time length velocity This distance can be reduced by cooling the wire in a water or oil bath. ( c ) The mass flow rate of the extruded wire through the air is kg/min 191 . m/min) 10 ( m) 0015 . ( ) kg/m 2702 ( ) 4 / ( 2 3 2 = = = = V r V m &amp; &amp; Then the rate of heat transfer from the wire to the air becomes W 856 = kJ/min 51.3 = C ) 50 350 )( C kJ/kg. 896 . )( kg/min 191 . ( ] ) ( [ = = T t T C m Q p &amp; &amp; 4-102...
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