Heat Chap09-072

Heat Chap09-072 - Chapter 9 Natural Convection Combined...

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Chapter 9 Natural Convection Combined Natural and Forced Convection 9-72C In combined natural and forced convection, the natural convection is negligible when Gr / Re . 2 01 < . Otherwise it is not. 9-73C In assisting or transverse flows, natural convection enhances forced convection heat transfer while in opposing flow it hurts forced convection. 9-74C When neither natural nor forced convection is negligible, it is not correct to calculate each separately and to add them to determine the total convection heat transfer. Instead, the correlation ( 29 n n n / 1 natural forced combined Nu Nu Nu + = based on the experimental studies should be used. 9-75 A vertical plate in air is considered. The forced motion velocity above which natural convection heat transfer from the plate is negligible is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The atmospheric pressure at that location is 1 atm. Properties The properties of air at 1 atm and 1 atm and the film temperature of ( T s + T )/2 = (85+30)/2 = 57.5 ° C are (Table A-15) 1 - 2 5 K 003026 . 0 K ) 273 5 . 57 ( 1 1 /s m 10 871 . 1 = + = = × = - f T β υ Analysis The characteristic length is the height of the plate, L c = L = 5 m. The Grashof and Reynolds numbers are - - × = × = = × = × - = - = V V L V L T T g Gr s 5 2 5 11 2 2 5 3 -1 2 2 3 10 67 . 2 /s m 10 871 . 1 ) m 5 ( Re 10 829 . 5 ) /s m 10 871 . 1 ( ) m 5 )( K 30 85 )( K 003026 . 0 )( m/s 81 . 9 ( ) ( and the forced motion velocity above which natural convection heat transfer from this plate is negligible is m/s 9.04 = → = × × = V V Gr 1 . 0 ) 10 67 . 2 ( 10 829 . 5 1 . 0 Re 2 5 11 2 9-71 Air T = 30 ° C V Plate, T s = 85 ° C L = 5 m

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Chapter 9 Natural Convection 9-76 "!PROBLEM 9-76" "GIVEN" L=5 "[m]" "T_s=85 [C], parameter to be varied" T_infinity=30 "[C]" "PROPERTIES" Fluid\$='air' rho=Density(Fluid\$, T=T_film, P=101.3) mu=Viscosity(Fluid\$, T=T_film) nu=mu/rho beta=1/(T_film+273) T_film=1/2*(T_s+T_infinity) g=9.807 "[m/s^2], gravitational acceleration" "ANALYSIS" Gr=(g*beta*(T_s-T_infinity)*L^3)/nu^2 Re=(Vel*L)/nu Gr/Re^2=0.1 T s [C] Vel [m/s] 50 5.598 55 6.233 60 6.801 65 7.318 70 7.793 75 8.233 80 8.646 85 9.033 90 9.4 95 9.747 100 10.08 105 10.39 110 10.69 115 10.98 120 11.26 125 11.53 130 11.79 135 12.03 140 12.27 145 12.51 150 12.73 9-72
Chapter 9 Natural Convection 50 70 90 110 130 150 5 6 7 8 9 10 11 12 13 T s [C] Vel [m/s] 9-73

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Chapter 9 Natural Convection 9-77 A vertical plate in water is considered. The forced motion velocity above which natural convection heat transfer from the plate is negligible is to be determined. Assumptions 1 Steady operating conditions exist. Properties The properties of water at the film temperature of ( T s + T )/2 = (60+25)/2 = 42.5 ° C are (Table A-15) υ β = × = - 0 65 10 0 00040 6 . . m / s K 2 -1 Analysis The characteristic length is the height of the plate L c = L = 5 m. The Grashof and Reynolds numbers are - - × = × = = × = × - = - = V V L V L T T g Gr s 6 2 6 13 2 2 6 3 -1 2 2 3 10 6 . 4 /s m 10 65 . 0 ) m 5 ( Re 10 063 . 4 ) /s m 10 65 . 0 ( ) m 5 )( K 25 60 )( K 0004 . 0 )( m/s 81 . 9 ( ) ( and the forced motion velocity above which natural convection heat transfer from this plate is negligible is m/s 2.62 = → = × × = V V Gr 1 . 0
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This homework help was uploaded on 03/19/2008 for the course ME 410 taught by Professor Benard during the Spring '08 term at Michigan State University.

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Heat Chap09-072 - Chapter 9 Natural Convection Combined...

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