Thermodynamics HW Solutions 392

Thermodynamics HW Solutions 392 - Bi < 0.1 s 204 =...

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Chapter 4 Transient Heat Conduction 4-123 Long copper 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 copper 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 copper are given to be k = 386 W/m. ° C, ρ = 8950 kg/m 3 , C p = 0.383 kJ/kg. ° C, and α = 1.13 × 10 -4 m 2 /s. Analysis ( a ) The characteristic length of the wire and the Biot number are 350 ° C 10 m/min Air 30 ° C Copper wire 1 . 0 000068 . 0 C W/m. 386 ) 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 < 0.1 s 204 = ⎯→ ⎯ = − − ⎯→ ⎯ = − − = ° ° = = = − − ∞ ∞ t e e T T T t T L C h V C hA b t bt i c p p s ) s 0136 . ( 1-3 2-1 30 350 30 50 ) ( s 0136 . m) C)(0.00075 J/kg. 383 )( kg/m (8950 C . W/m 35 ρρ ( b ) The wire travels a distance of m 34 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⎯→ ⎯ = s) (204 s/min 60 m/min 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 633 . m/min) 10 ( m) 0015 . ( ) kg/m 8950 ( ) 4 / ( 2 3 2 = = = = πρρ V r V m & & Then the rate of heat transfer from the wire to the air becomes W 1212 = kJ/min 72.7 = C ) 50 350 )( C kJ/kg. 383 . )( kg/min 633 . ( ] ) ( [ ° − ° = − = ∞ T t T C m Q p & & 4-103...
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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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