Thermodynamics HW Solutions 973

Thermodynamics HW Solutions 973 - 7256 . 861 . 7256 . C)...

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Chapter 12 Radiation Heat Transfer 12-92 Two concentric spheres which are maintained at uniform temperatures are separated by air at 1 atm pressure. The rate of heat transfer between the two spheres by natural convection and radiation is to be determined. Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Air is an ideal gas with constant properties. Properties The emissivities of the surfaces are given to be ε 1 = ε 2 = 0.5. The properties of air at 1 atm and the average temperature of ( T 1 + T 2 )/2 = (350+275)/2 = 312.5 K = 39.5 ° C are (Table A-15) 1 - 2 5 K 0032 . 0 K 5 . 312 1 7256 . 0 Pr /s m 10 697 . 1 C W/m. 02658 . 0 = = = × = ° = β υ k Analysis ( a ) Noting that D i = D 1 and D o = D 2 , the characteristic length is D 2 = 25 cm T 2 = 275 K ε 2 = 0.5 D 1 = 15 cm T 1 = 350 K ε 1 = 0.9 L c =5 cm AIR 1 atm m 0.05 m) 0.15 m 25 . 0 ( 2 1 ) ( 2 1 = = = i o c D D L Then 5 2 2 5 3 -1 2 2 3 2 1 10 415 . 7 ) 7256 . 0 ( ) /s m 10 697 . 1 ( ) m 05 . 0 )( K 275 350 )( K 003200 . 0 )( m/s 81 . 9 ( Pr ) ( × = × = = c L T T g Ra The effective thermal conductivity is [] [] 005900 . 0 m) 25 . 0 ( m) 15 . 0 ( m) 25 . 0 ( m) 15 . 0 ( m 05 . 0 ) ( ) ( 5 7/5 - 7/5 - 4 5 5 / 7 5 / 7 4 sph = + = + = o i o i c D D D D L F [] C W/m. 1315 ) 10 415 . 7 )( 00590 . 0 (
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Unformatted text preview: 7256 . 861 . 7256 . C) W/m. 02658 . ( 74 . ) ( Pr 861 . Pr 74 . 4 / 1 5 4 / 1 4 / 1 4 / 1 eff = + = + = Ra F k k sph Then the rate of heat transfer between the spheres becomes W 23.3 = = = K ) 275 350 ( ) m 05 . ( ) m 25 . )( m 15 . ( ) C W/m. 1315 . ( ) ( eff o i c o i T T L D D k Q & ( b ) The rate of heat transfer by radiation is determined from W 32.3 = + = + = = = = 2 4 4 4 2 8 2 2 2 1 2 2 1 4 1 4 2 1 12 2 2 2 1 1 25 . 15 . 9 . 9 . 1 9 . 1 ] ) K 275 ( ) K 350 )[( K W/m 10 67 . 5 )( m 0707 . ( 1 1 ) ( m 0707 . ) m 15 . ( D D T T A Q D A & 12-70...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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