Thermodynamics HW Solutions 770

Thermodynamics HW Solutions 770 - 2 2 5 3-1 2 2 3 = × −...

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Chapter 9 Natural Convection 9-101 A solar collector consists of a horizontal copper tube enclosed in a concentric thin glass tube. Water is heated in the tube, and the annular space between the copper and glass tube is filled with air. The rate of heat loss from the collector by natural convection is to be determined. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 Radiation effects are negligible. 3 The pressure of air in the enclosure is 1 atm. Properties The properties of air at 1 atm and the average temperature of ( T i + T o )/2 = (60+32)/2 = 46 ° C are (Table A-15) D o =9 cm D i =5 cm, T i = 60 ° C Air space Glass cover T o = 32 ° C 1 - 2 5 K 003135 . 0 K ) 273 46 ( 1 1 7239 . 0 Pr /s m 10 759 . 1 C W/m. 02706 . 0 = + = = β = × = υ ° = f T k Analysis The characteristic length in this case is the distance between the two cylinders , cm 2 2 cm ) 5 9 ( 2 = = = i o c D D L and, 106 , 16 ) 7239 . 0 ( ) /s m 10 759 . 1 ( ) m 02 . 0 )( K 32 60 )( K 003135 . 0 )( m/s 81 . 9 ( Pr ) (
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Unformatted text preview: 2 2 5 3-1 2 2 3 = × − = − = − υ β c o i L T T g Ra The effective thermal conductivity is [ ] 1303 . m) 09 . ( m) 05 . ( m) 02 . ( m 05 . m 09 . ln ) ( ln 5 7/5-7/5-3 4 5 5 / 3 5 / 3 3 4 cyl = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = − − o i c i o D D L D D F [ ] C W/m. 05812 . ) 106 , 16 )( 1303 . ( 7239 . 861 . 7239 . ) C W/m. 02706 . ( 386 . ) Ra ( Pr 861 . Pr 386 . 4 / 1 4 / 1 4 / 1 cyl 4 / 1 eff ° = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ° = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = F k k Then the heat loss from the collector per meter length of the tube becomes W 17.4 = ° − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ° = − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ = C ) 32 60 ( m 05 . m 09 . ln ) C W/m. 05812 . ( 2 ) ( ln 2 eff π o i i o T T D D k Q & 9-93...
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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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