Thermodynamics HW Solutions 706

Thermodynamics HW Solutions 706 - Chapter 9 Natural...

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Chapter 9 Natural Convection 9-19E A hot plate with an insulated back is considered. The rate of heat loss by natural convection is to be determined for different orientations. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. Properties The properties of air at 1 atm and the film temperature of ( T s + T )/2 = (130+75)/2 = 102.5 ° F are (Table A-15) 1 - 2 3 R 001778 . 0 R ) 460 5 . 102 ( 1 1 7256 . 0 Pr /s ft 10 1823 . 0 F Btu/h.ft. 01535 . 0 = + = = = × = ° = f T k β υ Analysis ( a ) When the plate is vertical, the characteristic length is the height of the plate. Then, ft. 2 = = L L c 8 2 2 3 3 -1 2 2 3 10 503 . 5 ) 7256 . 0 ( ) /s ft 10 1823 . 0 ( ) ft 2 )( R 75 130 )( R 001778 . 0 )( ft/s 2 . 32 ( Pr ) ( × = × = = L T T g Ra s 6 . 102 7256 . 0 492 . 0 1 ) 10 503 . 5 ( 387 . 0 825 . 0 Pr
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