Thermodynamics HW Solutions 949

Thermodynamics HW Solutions 949 - Chapter 12 Radiation Heat...

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Chapter 12 Radiation Heat Transfer 12-59 A coaxial radiation shield is placed between two coaxial cylinders which are maintained at uniform temperatures. The net rate of radiation heat transfer between the two cylinders is to be determined and compared with that without the shield. Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is not considered. Properties The emissivities of surfaces are given to be ε 1 = 0.7, ε 2 = 0.4. and ε 3 = 0.2. Analysis The surface areas of the cylinders and the shield per unit length are 2 3 3 shield 2 2 2 outer pipe, 2 1 1 inner pipe, m 942 . 0 ) m 1 )( m 3 . 0 ( m 314 . 0 ) m 1 )( m 1 . 0 ( m 628 . 0 ) m 1 )( m 2 . 0 ( = = = = = = = = = = = = ππ L D A A L D A A L D A A The net rate of radiation heat transfer between the two cylinders with a shield per unit length is W 703 = + + + + × = + + + + + = ) 4 . 0 )( 942 . 0 ( 4 . 0 1 ) 1 )( 628 . 0 ( 1 ) 2 . 0 )( 628 . 0 ( 2 . 0 1 2 ) 1 )( 314 . 0 ( 1 )
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