Thermodynamics HW Solutions 301

Thermodynamics HW Solutions 301 - ° F Analysis The...

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Chapter 4 Transient Heat Conduction 4-22 Ball bearings leaving the oven at a uniform temperature of 900 ° C are exposed to air for a while before they are dropped into the water for quenching. The time they can stand in the air before their temperature falls below 850 ° C is to be determined. Assumptions 1 The bearings are spherical in shape with a radius of r 0 = 0.6 cm. 2 The thermal properties of the bearings 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 bearings are given to be k = 15.1 W/m. ° C, ρ = 8085 kg/m 3 , and C p = 0.480 kJ/kg.
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Unformatted text preview: ° F. Analysis The characteristic length of the steel ball bearings and Biot number are 0.1 < 0166 . ) C W/m. 1 . 15 ( ) m 002 . )( C . W/m 125 ( m 002 . 6 m 012 . 6 6 / 2 2 3 = ° ° = = = = = = = k hL Bi D D D A V L c s c π Steel balls 900 ° C Air, 30 ° C Furnace Therefore, the lumped system analysis is applicable. Then the allowable time is determined to be s 3.68 = ⎯→ ⎯ = − − ⎯→ ⎯ = − − = ° ° = = = − − ∞ ∞ t e e T T T t T L C h V C hA b t bt i c p p s ) s 0161 . ( 1-3 2-1 30 900 30 850 ) ( s 01610 . m) C)(0.002 J/kg. 480 )( kg/m 8085 ( C . W/m 125 ρρ The result indicates that the ball bearing can stay in the air about 4 s before being dropped into the water. 4-12...
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