Heat Chap07-052

# Heat Chap07-052 - Chapter 7 External Forced Convection 7-52...

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Unformatted text preview: Chapter 7 External Forced Convection 7-52 A steam pipe is exposed to a light winds in the atmosphere. The amount of heat loss from the steam during a certain period and the money the facility will save a year as a result of insulating the steam pipe are to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The plant operates every day of the year for 10 h a day. 4 The local atmospheric pressure is 1 atm. Properties The properties of air at 1 atm and the film temperature of (T s + T ∞ )/2 = (75+5)/2 = 40 ° C are (Table A-15) 7255 . Pr /s m 10 702 . 1 C W/m. 02662 . 2 5- = × = ° = υ k Analysis The Reynolds number is [ ] 4 2 5 10 632 . 1 /s m 10 702 . 1 m) (0.1 m/s 1000/3600) (10 Re × = × × = υ =- ∞ D V The Nusselt number corresponding this Reynolds number is determined to be [ ] [ ] 19 . 71 000 , 282 10 632 . 1 1 ) 7255 . / 4 . ( 1 ) 7255 . ( ) 10 632 . 1 ( 62 . 3 . 000 , 282 Re 1 Pr) / 4 . ( 1 Pr Re 62 . 3 . 5 / 4 8 / 5 4 4 / 1 3 / 2 3 / 1 5 . 4 5 / 4 8 / 5 4 / 1 3 / 2 3 / 1 5 . = × + + × + = + + + = = k hD Nu The heat transfer coefficient is C . W/m 95 . 18 ) 19 . 71 ( m 1 . C W/m. 02662 . 2 ° = ° = = Nu D k h The rate of heat loss by convection is 2 m 77 . 3 m) 12 )( m 1 . ( = = = π π DL A s W 5001 = C 5)- )(75 m C)(3.77 . W/m 95 . 18 ( ) ( 2 2 ° ° =- = ∞ T T hA Q s s The rate of heat loss by radiation is [ ] W 1558 ) K 273 ( ) K 273 75 ( ) .K W/m 10 )(5.67 m (3.77 ) 8 . ( ) ( 4 4 4 2-8 2 4 4 = +- + × =- = surr s s rad T T A Q σ ε The total rate of heat loss then becomes W 6559 1558 5001 total = + = + = rad conv Q Q Q The amount of heat loss from the steam during a 10-hour work day is kJ/day 10 2.361 5 × = × = ∆ = ) s/h 3600 h/day 10 )( kJ/s 559 . 6 ( t Q Q total The total amount of heat loss from the steam per year is kJ/yr 10 619 . 8 ) days/yr 365 )( kJ/day 10 361 . 2 ( ) days of no. ( 7 5 × = × = = day total Q Q Noting that the steam generator has an efficiency of 80%, the amount of gas used is therms/yr 1021 kJ 105,500 therm 1 80 . kJ/yr 10 619 . 8 80 . 7 = × = = total gas Q Q Insulation reduces this amount by 90 %. The amount of energy and money saved becomes therms/yr 919 = ) therms/yr 1021 )( 90 . ( ) 90 . ( saved Energy = = gas Q \$496 = = erm) )(\$0.54/th therms/yr (919 = energy) of cost t saved)(Uni Energy ( saved Money 7-36 Wind V ∞ = 10 km/h T ∞ = 5 ° C Steam pipe T s = 75 ° C D = 10 cm ε = 0.8 Chapter 7 External Forced Convection 7-53 A steam pipe is exposed to light winds in the atmosphere. The amount of heat loss from the steam during a certain period and the money the facility will save a year as a result of insulating the steam pipes are to be determined....
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Heat Chap07-052 - Chapter 7 External Forced Convection 7-52...

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