Thermodynamics HW Solutions 584

Thermodynamics HW Solutions 584 - + + + = + + + = = k hD Nu...

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Chapter 7 External Forced Convection 7-54E An electrical resistance wire is cooled by a fan. The surface temperature of the wire is 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 local atmospheric pressure is 1 atm. Properties We assume the film temperature to be 200 ° . The properties of air at this temperature are (Table A-15E) F 7124 . 0 Pr /s ft 10 2406 . 0 F Btu/h.ft. 01761 . 0 2 3 - = × = ° = υ k Air V = 20 ft/s T = 85 ° F Resistance wire D = 0.1 in Analysis The Reynolds number is 8 . 692 /s ft 10 2406 . 0 ft) 12 ft/s)(0.1/ (20 Re 2 3 = × = = D V The proper relation for Nusselt number corresponding this Reynolds number is [] [] 34 . 13 000 , 282 8 . 692 1 ) 7124 . 0 / 4 . 0 ( 1 ) 7124 . 0 ( ) 8 . 692 ( 62 . 0 3 . 0 000 , 282 Re 1 Pr) / 4 . 0 ( 1 Pr Re 62 . 0 3 . 0 5 / 4 8 / 5 4 / 1 3 / 2 3 / 1 5 . 0 5 / 4 8 / 5 4 / 1 3 / 2 3 / 1 5 . 0 =
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Unformatted text preview: + + + = + + + = = k hD Nu The heat transfer coefficient is F . Btu/h.ft 19 . 28 ) 34 . 13 ( ft) 12 / 1 . ( F Btu/h.ft. 01761 . 2 = = = Nu D k h Then the average temperature of the outer surface of the wire becomes 2 ft 3142 . ft) 12 )( ft 12 / 1 . ( = = = DL A s F 662.9 = = + = = ) ft F)(0.3142 . Btu/h.ft 19 . 28 ( Btu/h 3.41214) (1500 + F 85 ) ( 2 2 hA Q T T T T hA Q s s s & & Discussion Repeating the calculations at the new film temperature of (85+662.9)/2=374 F gives T s =668.3 F. 7-39...
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