Thermodynamics HW Solutions 283

# Thermodynamics HW Solutions 283 - Chapter 3 Steady Heat...

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Chapter 3 Steady Heat Conduction 3-172 Steam is flowing inside a steel pipe. The thickness of the insulation needed to reduce the heat loss by 95 percent and the thickness of the insulation needed to reduce outer surface temperature to 40 ° C are to be determined. Assumptions 1 Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the centerline and no variation in the axial direction. 3 Thermal conductivities are constant. 4 The thermal contact resistance at the interface is negligible. Properties The thermal conductivities are given to be k = 61 W/m °C for steel and k = 0.038 W/m °C for insulation. Analysis ( a ) Considering a unit length of the pipe, the inner and the outer surface areas of the pipe and the insulation are 2 3 3 3 3 2 2 2 1 m 1416 . 3 m) 1 ( m 3770 . 0 m) 1 ( m) 12 . 0 ( m 3142 . 0 m) 1 ( m) 10 . 0 ( D D L D A L D A L D A o i = π = π = = π = π = = π = π = R i T 1 R 2 R o T 2 R 1 The individual thermal resistances are C/W 02274 . 0 0.23876 ) 12 . 0 / ln( 03079 . 0 02274 . 0 0.23876 ) 12 . 0 / ln( 00048 . 0 03031 . 0 C/W 22026 . 0 18947 . 0 00048 . 0 03031 . 0 C/W 02274 . 0 ) m 1416 . 3 ( C) . W/m 14 ( 1 1 C/W 18947 . 0 ) m 3770 . 0 ( C) . W/m 14 ( 1 1 C/W 0.23876 ) 12 . 0 / ln( ) m 1 ( C) W/m. 038 .
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