Thermodynamics HW Solutions 978

Thermodynamics HW Solutions 978 - = − υ L T T g Ra 539 ....

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Chapter 12 Radiation Heat Transfer 12-95 A double-pane window consists of two sheets of glass separated by an air space. The rates of heat transfer through the window by natural convection and radiation are to be determined. Assumptions 1 Steady operating conditions exist 2 The surfaces are opaque, diffuse, and gray. 3 Air is an ideal gas with constant specific heats. 4 Heat transfer through the window is one-dimensional and the edge effects are negligible. 5 ° C 15 ° C L = 5 cm H = 2 m Q Air Properties The emissivities of glass surfaces are given to be ε 1 = ε 2 = 0.9. The properties of air at 0.3 atm and the average temperature of ( T 1 + T 2 )/2 = (15+5)/2 = 10 ° C are (Table A-15) 1 - 2 5 5 1 K 003534 . 0 K ) 273 10 ( 1 7336 . 0 Pr /s m 10 753 . 4 /0.3 10 426 . 1 3 . 0 / C W/m. 02439 . 0 = + = = × = × = = ° = β υυ atm k Analysis The characteristic length in this case is the distance between the glasses, m 05 . 0 = = L L c 4 2 2 5 3 -1 2 2 3 2 1 10 918 . 1 ) 7336 . 0 ( ) /s m 10 753 . 4 ( ) m 05 . 0 ( K ) 5 15 )( K 003534 . 0 )( m/s 81 . 9 ( Pr ) ( × = × =
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Unformatted text preview: = − υ L T T g Ra 539 . 1 05 . 2 ) 10 918 . 1 ( 197 . 197 . 9 / 1 4 / 1 4 9 / 1 4 / 1 = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ × = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − − L H Ra Nu 2 m 6 ) m 3 )( m 2 ( = = s A Then the rate of heat transfer by natural convection becomes W 45.0 = ° − ° = − = m 05 . C ) 5 15 ( ) m 6 )( 539 . 1 )( C W/m. 02439 . ( 2 2 1 L T T kNuA Q s conv & The rate of heat transfer by radiation is determined from ( ) ( ) W 252 = − + + − + ⋅ × = − + − = − 1 9 . 1 9 . 1 ] K 273 5 K 273 15 )[ K W/m 10 67 . 5 )( m 6 ( 1 1 1 ) ( 4 4 4 2 8 2 2 1 4 2 4 1 rad εε σ T T A Q s & Then the rate of total heat transfer becomes W 297 = + = + = 252 45 rad conv total Q Q Q & & & Discussion Note that heat transfer through the window is mostly by radiation. 12-75...
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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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