Thermodynamics HW Solutions 566

Thermodynamics HW Solutions 566 - Chapter 7 External Forced...

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Chapter 7 External Forced Convection 7-40 A hot stainless steel ball is cooled by forced air. The average convection heat transfer coefficient and the cooling time are to be determined. Assumptions 1 Steady operating conditions exist. 2 Radiation effects are negligible. 3 Air is an ideal gas with constant properties. 4 The outer surface temperature of the ball is uniform at all times. Properties The average surface temperature is (350+250)/2 = 300 ° C, and the properties of air at 1 atm pressure and the free stream temperature of 30 ° C are (Table A-15) 7282 . 0 Pr kg/m.s 10 934 . 2 kg/m.s 10 872 . 1 /s m 10 608 . 1 C W/m. 02588 . 0 5 C 300 @ , 5 2 5 - = × = × = × = ° = ° s k μ υ Air V = 6 m/s T = 30 ° C D = 15 cm T s = 350 ° C D Analysis The Reynolds number is 4 2 5 10 597 . 5 /s m 10 57 . 1 m) m/s)(0.15 (6 Re × = × = υ = D V The Nusselt number corresponding this Reynolds number is determined to be [] 6 . 145 10 934 . 2 10 872 . 1 ) 7282 . 0 ( ) 10 597 . 5 ( 06 . 0 ) 10 597 . 5 ( 4 . 0 2 Pr Re 06 . 0 Re 4 . 0 2 4 / 1 5 5 4 . 0 3 / 2 4 5 . 0 4 4 / 1 4 . 0 3 / 2 5 . 0 = × × × + × + = μ μ + + = = s k hD Nu Heat transfer coefficient is
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