Thermodynamics HW Solutions 726

Thermodynamics HW Solutions 726 - Chapter 9 Natural...

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Chapter 9 Natural Convection Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. L = 13 ft Furnace ε = 0.1 Air T = 75 ° F D = 8 ft Properties The properties of air at 1 atm and the anticipated film temperature of ( T s + T )/2=(140+75)/2=107.5 ° F are (Table A-15) 1 - 2 3 R 001762 . 0 R ) 460 5 . 107 ( 1 1 7249 . 0 Pr /s ft 10 1851 . 0 F Btu/h.ft. 01546 . 0 = + = = = × = ° = f T k β υ Analysis The solution of this problem requires a trial-and-error approach since the determination of the Rayleigh number and thus the Nusselt number depends on the surface temperature which is unknown. We start the solution process by “guessing” the surface temperature to be 140 ° F for the evaluation of the properties and h . We will check the accuracy of this guess later and repeat the calculations if necessary. The characteristic length in this case is the outer diameter of the furnace,
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