Thermodynamics HW Solutions 929

# Thermodynamics HW Solutions 929 - of radiation heat...

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Chapter 12 Radiation Heat Transfer 12-38 A spherical tank filled with liquid nitrogen is kept in an evacuated cubic enclosure. The net rate of radiation heat transfer to the liquid nitrogen is to be determined. Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is not considered. 4 The thermal resistance of the tank is negligible. Properties The emissivities of surfaces are given to be ε 1 = 0.1 and ε 2 = 0.8. Analysis We take the sphere to be surface 1 and the surrounding cubic enclosure to be surface 2. Noting that F 12 1 = , for this two-surface enclosure, the net rate of radiation heat transfer to liquid nitrogen can be determined from ( ) [] () () () [] W 228 = + × = + = = 2 2 4 4 4 2 8 2 2 1 2 2 1 4 2 4 1 1 12 21 m) 6(3 m) 2 ( 8 . 0 8 . 0 1 1 . 0 1 K 240 K 100 K W/m 10 67 . 5 m) 2 ( 1 1 π ε σ A A T T A Q Q Cube, a =3 m T 2 = 240 K ε 2 = 0.8 D 1 = 2 m T 1 = 100 K ε 1 = 0.1 Vacuum Liquid N 2 12-39 A spherical tank filled with liquid nitrogen is kept in an evacuated spherical enclosure. The net rate
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Unformatted text preview: of radiation heat transfer to the liquid nitrogen is to be determined. Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Convection heat transfer is not considered. 4 The thermal resistance of the tank is negligible. Properties The emissivities of surfaces are given to be ε 1 = 0.1 and ε 2 = 0.8. D 2 = 3 m T 2 = 240 K ε 2 = 0.8 D 1 = 2 m T 1 = 100 K ε 1 = 0.1 Vacuum Liquid N 2 Analysis The net rate of radiation heat transfer to liquid nitrogen can be determined from ( ) ( ) W 227 = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + − ⋅ × = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − + − = − 2 2 4 4 4 2 8 2 2 2 2 1 2 2 1 4 2 4 1 1 12 m) (1.5 m) 1 ( 8 . 8 . 1 1 . 1 ] K 100 K 240 )[ K W/m 10 67 . 5 ]( m) 2 ( [ 1 1 ) ( r r T T A Q & 12-26...
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