Thermodynamics HW Solutions 739

# Thermodynamics HW Solutions 739 - m/s 81 9 Pr × = × − =...

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Chapter 9 Natural Convection 9-44 The equilibrium temperature of a light glass bulb in a room is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 The light bulb is approximated as an 8-cm-diameter sphere. Properties The solution of this problem requires a trial-and-error approach since the determination of the Rayleigh number and thus the Nusselt number depends on the surface temperature which is unknown. We start the solution process by “guessing” the surface temperature to be 170 ° C for the evaluation of the properties and h . We will check the accuracy of this guess later and repeat the calculations if necessary. The properties of air at 1 atm and the anticipated film temperature of ( T s + T )/2 = (170+25)/2 = 97.5 ° C are (Table A-15) 1 - 2 5 K 002699 . 0 K ) 273 5 . 97 ( 1 1 7116 . 0 Pr /s m 10 279 . 2 C W/m. 03077 . 0 = + = = β = × = υ ° = f T k Analysis The characteristic length in this case is L c = D = 0.08 m. Then, 6 2 2 5 3 -1 2 2 3 10 694 . 2 ) 7116 . 0 ( ) /s m 10 279 . 2 ( ) m 08 . 0 )( K 25 170 )( K 002699
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Unformatted text preview: . )( m/s 81 . 9 ( Pr ) ( × = × − = − = − ∞ υ β D T T g Ra s Air T ∞ = 25 ° C Lamp 60 W ε = 0.9 D = 8 cm Light, 6 W ( ) [ ] ( ) [ ] 42 . 20 7116 . / 469 . 1 ) 10 694 . 2 ( 589 . 2 Pr / 469 . 1 589 . 2 9 / 4 16 / 9 4 / 1 6 9 / 4 16 / 9 4 / 1 = + × + = + + = Ra Nu Then 2 2 2 2 m 02011 . m) 08 . ( C . W/m 854 . 7 ) 42 . 20 ( m 08 . C W/m. 03077 . = = = ° = ° = = ππ D A Nu D k h s Considering both natural convection and radiation, the total rate of heat loss can be written as ] ) K 273 25 ( ) 273 )[( .K W/m 10 67 . 5 )( m 02011 . )( 9 . ( C ) 25 )( m 02011 . )( C . W/m 854 . 7 ( W ) 60 90 . ( ) ( ) ( 4 4 4 2 8 2 2 2 4 4 + − + × + ° − ° = × − + − = − ∞ s s surr s s s s T T T T A T T hA Q σε & Its solution is T s = 169.4 ° C which is sufficiently close to the value assumed in the evaluation of properties and h . Therefore, there is no need to repeat calculations. 9-40...
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