HW4 Solutions

# HW4 Solutions - ME 364 Spring 2008 HW 4 Solutions Problem 1...

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ME 364, Spring 2008 HW 4 Solutions Problem 1: Two cast iron steam pipes are connected to each other through two 1-cm thick flanges exposed to cold ambient air. The average outer surface temperature of the pipe, the fin efficiency, the rate of heat transfer from the flanges, and the equivalent pipe length of the flange for heat transfer are to be determined. Assumptions 1 Steady operating conditions exist. 2 The temperature along the flanges (fins) varies in one direction only (normal to the pipe). 3 The heat transfer coefficient is constant and uniform over the entire fin surface. 4 The thermal properties of the fins are constant. 5 The heat transfer coefficient accounts for the effect of radiation from the fins. Properties The thermal conductivity of the cast iron is given to be k = 52 W/m °C. Analysis ( a ) We treat the flanges as fins. The individual thermal resistances are 2 2 m 88 . 1 m) 6 ( m) 1 . 0 ( m 73 . 1 m) 6 ( m) 092 . 0 ( L D A L D A o o i i C/W 0213 . 0 ) m 88 . 1 ( C) . W/m 25 ( 1 1 C/W 00004 . 0 ) m 6 ( C) W/m. 52 ( 2 ) 6 . 4 / 5 ln( 2 ) / ln( C/W 0032 . 0 ) m 73 . 1 ( C) . W/m 180 ( 1 1 2 2 o 1 2 cond 2 2 i o o i i A h R kL r r R A h R C/W 0245 . 0 0213 . 0 00004 . 0 0032 . 0 o cond i total R R R R The rate of heat transfer and average outer surface temperature of the pipe are C 175.4 C/W) 0213 . 0 )( W 7673 ( C 12 W 7673 C 0.0245 C ) 12 200 ( o 2 2 o 2 2 total 2 1 R Q T T R T T Q R T T Q ( b ) The fin efficiency can be determined from (Fig. 3-43) 88 . 0 29 . 0 m) C)(0.02 W/m 52 ( C W/m 25 m 2 02 . 0 m 05 . 0 2 2 . 2 05 . 0 2 02 . 0 1 . 0 2 fin o o 2 2 / 1 2 / 3 1 2 kt h t L kA h L r t r p c 2 2 2 2 2 1 2 2 fin m 0597 . 0 m) m)(0.02 1 . 0 ( 2 ] m) 05 . 0 ( m) 1 . 0 [( 2 2 ) ( 2 t r r r A The heat transfer rate from the flanges is W 215 C ) 12 4 . 175 )( m 0597 . 0 )( C . W/m 25 ( 88 . 0 ) ( 2

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HW4 Solutions - ME 364 Spring 2008 HW 4 Solutions Problem 1...

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