Thermodynamics HW Solutions 302

Thermodynamics HW Solutions 302 - Chapter 4 Transient Heat...

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Chapter 4 Transient Heat Conduction 4-23 A number of carbon steel balls are to be annealed by heating them first and then allowing them to cool slowly in ambient air at a specified rate. The time of annealing and the total rate of heat transfer from the balls to the ambient air are to be determined. Assumptions 1 The balls are spherical in shape with a radius of r 0 = 4 mm. 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 balls are given to be k = 54 W/m. ° C, ρ = 7833 kg/m 3 , and C p = 0.465 kJ/kg. ° C. Analysis The characteristic length of the balls and the Biot number are 1 . 0 0018 . 0 ) C W/m. 54 ( ) m 0013 . 0 )( C . W/m 75 ( m 0013 . 0 6 m 008 . 0 6 6 / 2 2 3 < = ° ° = = = = = =
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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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