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Thermodynamics HW Solutions 787

# Thermodynamics HW Solutions 787 - 71 m 429 C W/m 02588 = =...

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Chapter 9 Natural Convection 9-113 A flat-plate solar collector tilted 40 ° C from the horizontal is exposed to the calm ambient air. The total rate of heat loss from the collector, the collector efficiency, and the temperature rise of water in the collector are 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 There is no heat loss from the back surface of the absorber plate. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (40+20)/2 = 30 ° C are (Table A-15) 1 - 2 5 K 0033 . 0 K ) 273 30 ( 1 1 7282 . 0 Pr /s m 10 608 . 1 C W/m. 02588 . 0 = + = = = × = ° = f T k β υ Analysis ( a ) The characteristic length in this case is determined from Solar radiation 650 W/m 2 θ =40 ° Insulation Absorber Plate Glass Cover, 40 ° C 1.5 m δ = 3 cm Outdoors, T = 20 ° C T sky = -40 ° C 2 m 429 . 0 m) 2 + m 2(1.5 ) m 2 )( m 5 . 1 ( = = = p A L s c Then, 8 2 2 5 3 -1 2 2 3 10 100 . 1 ) 7282 . 0 ( ) /s m 10 608 . 1 ( ) m 429 . 0 )( K 20 40 )( K 003311 . 0 )( 40 )(cos m/s 81 . 9 ( Pr ) ( × = × ° = = c s L T T g Ra 87 . 71 ) 10 100 . 1 ( 15 . 0 15 . 0 3 / 1 8 3 / 1 = × = = Ra Nu 2 2 m 3 ) m 2 )( m 5 . 1 ( C . W/m 340 . 4 ) 87
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Unformatted text preview: . 71 ( m 429 . C W/m. 02588 . = = ° = ° = = s s A Nu L k h and W 4 . 260 C ) 20 40 )( m 3 )( C . W/m 340 . 4 ( ) ( 2 2 = ° − ° = − = ∞ T T hA Q s s conv & Heat transfer rate by radiation is W 1018 ] ) K 273 40 ( ) K 273 40 )[( .K W/m 10 67 . 5 )( m 3 )( 9 . ( ) ( 4 4 4 2 8 2 4 4 = + − − + × = − = − s surr s rad T T A Q σε & and W 1279 = + = 1018 4 . 260 total Q & ( b ) The solar energy incident on the collector is W 1716 ) m 3 )( W/m 650 )( 88 . ( 2 2 = = = s incident A q Q & & α Then the collector efficiency becomes 25.5% = = − = − = 255 . 1716 1279 1716 incident lost incident Q Q Q efficiency & & & ( c ) The temperature rise of the water as it passes through the collector is C 6.3 ° = ° − = = Δ → Δ = C) J/kg. 4180 )( kg/s 60 / 1 ( W ) 1279 1716 ( p p C m Q T T C m Q & & & & 9-111...
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