Thermodynamics HW Solutions 740

Thermodynamics HW Solutions 740 - Chapter 9 Natural...

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Chapter 9 Natural Convection 9-45 A vertically oriented cylindrical hot water tank is located in a bathroom. The rate of heat loss from the tank by natural convection and radiation is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 The temperature of the outer surface of the tank is constant. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (44+20)/2 = 32 ° C are (Table A-15) 1 - 2 5 K 003279 . 0 K ) 273 32 ( 1 1 7276 . 0 Pr /s m 10 627 . 1 C W/m. 02603 . 0 = + = = = × = ° = f T k β υ Analysis The characteristic length in this case is the height of the cylinder, Air T = 20 ° C Tank T s = 44 ° C ε = 0.4 L = 1.1 m D = 0.4 m m. 1 . 1 = = L L c Then, 9 2 2 5 3 -1 2 2 3 10 883 . 3 ) /s m 10 627 . 1 ( ) m 1 . 1 )( K 20 44 )( K 003279 . 0 )( m/s 81 . 9 ( ) ( Gr × = × = = L T T g s A vertical cylinder can be treated as a vertical plate when
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