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
-5
2
υ = 1.426 × 10 m /s
Pr = 0.7336
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
hD
0.62 Re 0.5 Pr 1 / 3
Nu =
= 0.3 +
1/ 4
k
1 + (0.4 / Pr )2 / 3
[
]
  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  

= 0.3 +
+
1
= 36.0



 
1/ 4
  282,000  
1 + (0.4 / 0.7336)2 / 3
The heat transfer coefficient is
k
0.02439 W/m.°C
h = Nu =
(36.0) = 146.3 W/m 2 .°C
D
0.006 m
The rate of heat generated in the electrical transmission lines per meter length is
W& = Q& = I 2 R = (50 A) 2 (0.002 Ohm) = 5.0 W
[
]
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 = πDL = π (0.006 m)(1 m) = 0.01885 m 2
Q&
5W
Q& = hAs (Ts − T∞ ) 
→ Ts = T∞ +
= 10°C +
= 11.8°C
2
hAs
(146.3 W/m .°C)(0.01885 m 2 )