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7-46 The wind is blowing across the wire of a transmission line. 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 10°C. The properties of air at this temperature are (Table A-15)

ρ = 1.246 kg/m 3 k = 0.02439 W/m.°C

υ = 1.426 × 10 m /s Pr = 0.7336 -5

2

Analysis The Reynolds number is V D [(40 ×1000/3600) m/s ](0.006 m) Re = ∞ = = 4674 υ 1.426 ×10 − 5 m 2 /s The Nusselt number corresponding this Reynolds number is determined to be 0.5

1/ 3

0.62 Re Pr hD = 0.3 + Nu = 2 / 3 1/ 4 k 1 + (0.4 / Pr)

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  Re  5 / 8  1 +      282,000  

Wind V∞ = 40 km/h T∞ = 10°C

Transmission wire, Ts D = 0.6 cm

4/5

4/5

5/ 8 0.62(4674) 0.5 (0.7336)1 / 3   4674    = 36.0  + 1     2 / 3 1/ 4  282,000    1+ (0.4 / 0.7336 )   The heat transfer coefficient is 0.02439 W/m.° C k (36.0) = 146.3 W/m 2 . °C h = Nu = 0.006 m D The rate of heat generated in the electrical transmission lines per meter length is W& = Q& = I 2R = ( 50 A)2 (0.002 Ohm) = 5.0 W

= 0.3 +

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The entire heat generated in electrical transmission line has to be transferred to the ambient air. The surface temperature of the wire then becomes As = π DL = π(0.006 m)(1 m) = 0.01885 m 2 & Q 5W → Ts = T∞ + = 10°C + = 11.8°C Q& = hAs (Ts − T∞ )  2 hAs (146.3 W/m . °C)(0.01885 m 2 )...