Thermodynamics HW Solutions 710

Thermodynamics HW Solutions 710 - Chapter 9 Natural...

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Chapter 9 Natural Convection 9-21 A cylindrical resistance heater is placed horizontally in a fluid. The outer surface temperature of the resistance wire is to be determined for two different fluids. Assumptions 1 Steady operating conditions exist. 2 Air is an ideal gas with constant properties. 3 The local atmospheric pressure is 1 atm. 4 Any heat transfer by radiation is ignored. 5 Properties are evaluated at 500 ° C for air and 40 ° C for water. Properties The properties of air at 1 atm and 500 ° C are (Table A-15) 1 - 2 5 K 001294 . 0 K ) 273 500 ( 1 1 6986 . 0 Pr /s m 10 804 . 7 C W/m. 05572 . 0 = + = = β = × = υ ° = f T k Air T = 20 ° C Resistance heater, T s 400 W L =1 m D = 0.5 cm The properties of water at 40 ° C are 1 - 2 6 K 000377 . 0 32 . 4 Pr /s m 10 6582 . 0 / C W/m. 631 . 0 = β = × = ρ μ = υ ° = k Analysis ( a ) 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
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