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Heat Chap01-087 - Chapter 1 Basics of Heat Transfer 1-87E A...

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Chapter 1 Basics of Heat Transfer 1-87E A 200-ft long section of a steam pipe passes through an open space at a specified temperature. The rate of heat loss from the steam pipe and the annual cost of this energy lost are to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer by radiation is disregarded. 3 The convection heat transfer coefficient is constant and uniform over the surface. Analysis ( a ) The rate of heat loss from the steam pipe is 2 ft 4 . 209 ft) 200 ( ft) 12 / 4 ( = = = π π DL A s Btu/h 289,000 = F ) 50 280 )( ft 4 . 209 ( F) . Btu/h.ft 6 ( ) ( 2 2 pipe ° - ° = - = air s s T T hA Q ( b ) The amount of heat loss per year is Q Q t = = × = × ( , . 289 000 2 532 10 9 Btu / h)(365 24 h / yr) Btu / yr The amount of gas consumption per year in the furnace that has an efficiency of 86% is therms/yr 438 , 29 Btu 100,000 therm 1 86 . 0 Btu/yr 10 532 . 2 Loss Energy Annual 9 = × = Then the annual cost of the energy lost becomes Energy cost Annual energy loss)(Unit cost of energy) = (29,438 therms / yr) therm) = = ( ($0. / 58 $17,074 / yr 1-88 A 4-m diameter spherical tank filled with liquid nitrogen at 1 atm and -196 ° C is exposed to convection with ambient air. The rate of evaporation of liquid nitrogen in the tank as a result of the heat transfer from the ambient air is to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer by radiation is disregarded. 3 The convection heat transfer coefficient is constant and uniform over the surface. 4 The temperature of the thin-shelled spherical tank is nearly equal to the temperature of the nitrogen inside. Properties The heat of vaporization and density of liquid nitrogen at 1 atm are given to be 198 kJ/kg and 810 kg/m 3 , respectively. Analysis The rate of heat transfer to the nitrogen tank is 2 2 2 m 27 . 50 m) 4 ( = = = π π D A s W 271,430 = ° - - ° = - = C )] 196 ( 20 )[ m 27 . 50 ( C) . W/m 25 ( ) ( 2 2 air T T hA Q s s Then the rate of evaporation of liquid nitrogen in the tank is determined to be kg/s 1.37 = = = → = kJ/kg 198 kJ/s 430 . 271 fg fg h Q m h m Q 1-43 D =4 in 280 ° F L=200 ft Q Air,50 ° F 1 atm Liquid N 2 -196 ° C Q Vapor Air 20 ° C
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Chapter 1 Basics of Heat Transfer 1-89 A 4-m diameter spherical tank filled with liquid oxygen at 1 atm and -183 ° C is exposed to convection with ambient air. The rate of evaporation of liquid oxygen in the tank as a result of the heat transfer from the ambient air is to be determined. Assumptions 1 Steady operating conditions exist. 2 Heat transfer by radiation is disregarded. 3 The convection heat transfer coefficient is constant and uniform over the surface. 4 The temperature of the thin-shelled spherical tank is nearly equal to the temperature of the oxygen inside. Properties The heat of vaporization and density of liquid oxygen at 1 atm are given to be 213 kJ/kg and 1140 kg/m 3 , respectively.
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