Thermodynamics HW Solutions 722

Thermodynamics HW Solutions 722 - Chapter 9 Natural...

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Chapter 9 Natural Convection 9-29 An absorber plate whose back side is heavily insulated is placed horizontally outdoors. Solar radiation is incident on the plate. The equilibrium temperature of the plate is to be determined for two cases. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. Insulation Air T = 25 ° C Absorber plate α s = 0.98 ε = 0.98 700 W/m 2 L = 1.2 m Properties The properties of air at 1 atm and the anticipated film temperature of ( T s + T )/2 = (70+25)/2 = 47.5 ° C are (Table A-15) 1 - 2 5 K 00312 . 0 K ) 273 5 . 47 ( 1 1 7235 . 0 Pr /s m 10 774 . 1 C W/m. 02717 . 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 70 ° C for the evaluation of the properties and h . We will check the accuracy of this guess later and repeat the calculations if necessary.
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