hw2-solution - ME 324 HW#2 07.03.2011 1 Steam at 320C flows...

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ME 324 HW #2 07.03.2011 1. Steam at 320ºC flows in a case iron pipe ( k = 80 W/m ºC) whose inner and outer diameters are 5 cm and 5.5 cm, respectively. The pipe is covered with 3-cm-thick glass wool insulation with k = 0.05 W/m ºC. Heat is lost to the surroundings at 5ºC by natural convection and radiation, with a combined heat transfer coefficient of h = 18 W/m 2 K. Taking the heat transfer coefficient inside the pipe to be h = 60 W/m 2 K, determine (1) the rate of heat loss from the steam per unit length of the pipe, and (2) the temperature drop across the insulation. insulation T ∞,o r 2 T ∞,i r 1 r 3 m 025 . 0 1 r m 0275 . 0 2 r m 0575 . 0 3 r Let L = 1 m. Then 2 1 m 157 . 0 ) 1 )( 025 . 0 ( 2 2 L r A i 2 3 m 361 . 0 ) 1 )( 0575 . 0 ( 2 2 L r A o K/W 61 . 2 154 . 0 35 . 2 0002 . 0 106 . 0 ) 361 . 0 )( 18 ( 1 ) 1 )( 05 . 0 ( 2 ) 0275 . 0 / 0575 . 0 ln( ) 1 )( 80 ( 2 ) 025 . 0 / 0275 . 0 ln( ) 157 . 0 )( 60 ( 1 1 2 ) / ln( 2 ) / ln( 1 2 3 1 2 o o ins pipe i i total A h L k r r L k r r A h R W 121 61 . 2 5 320 2 , 1 , total R T T q K 284 ) 35 . 2 )( 121 (
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