Thermodynamics HW Solutions 697

Thermodynamics HW Solutions 697 - flow in the entire duct,...

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Chapter 8 Internal Forced Convection 8-75 Cold-air flows through an isothermal pipe. The pipe temperature is to be estimated. Assumptions 1 Steady operating conditions exist. 2 The inner surface of the duct is smooth. 3 Air is an ideal gas with constant properties. 4 The pressure of air is 1 atm. Properties The properties of air at 1 atm and the bulk mean temperature of (5+19) / 2 = 12 ° C are (Table A- 15) 20 m Air 5 ° C 2.5 m/s 12 cm T s 19 ° C 7331 . 0 Pr C J/kg. 1007 /s m 10 444 . 1 C W/m. 02454 . 0 kg/m 238 . 1 2 5 - 3 = ° = × = ° = = p C k υ ρ Analysis The rate of heat transfer to the air is m/s 03499 . 0 m/s) 5 . 2 ( 4 m) 12 . 0 ( ) kg/m 238 . 1 ( 2 3 = = = π m c A m V W 1 . 493 C ) 5 19 )( C J/kg. kg/s)(1007 03499 . 0 ( = ° ° = Δ = T C m Q p Reynolds number is 775 , 20 /s m 10 444 . 1 m) m/s)(0.12 (2.5 Re 2 5 = × = υ = D V which is greater than 10,000. Therefore, the flow is turbulent and the entry lengths in this case are roughly m 1.2 = m) 12 . 0 ( 10 10 = D L L t h which is much shorter than the total length of the duct. Therefore, we can assume fully developed turbulent
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Unformatted text preview: flow in the entire duct, and determine the Nusselt number from 79 . 57 ) 7331 . ( ) 775 , 20 ( 023 . Pr Re 023 . 4 . 8 . 4 . 8 . = = = = k hD Nu Heat transfer coefficient is C . W/m 82 . 11 ) 79 . 57 ( m 12 . C W/m. 02454 . 2 = = = Nu D k h The logarithmic mean temperature difference is determined from [ ] C 535 . 5 m) 20 ( m) 12 . ( ) C . W/m 82 . 11 ( W 1 . 493 ln ln 2 ln = = = T T T hA Q s & Then the pipe temperature is determined from the definition of the logarithmic mean temperature difference C 3.8 = = = s s s i s e s i e T T T T T T T T T T 5 19 ln 5 19 C 535 . 5 ln ln 8-59...
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This note was uploaded on 01/24/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.

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