Overhead electric transmission lines get heated (due to the electric resistivity of the cable material) and lose heat to the ambient air; this transmission energy loss due to heat transfer is referred to as the Joule effect in the conduction material. Consider a 3- cm diameter horizontal cable that dissipates heat at the rate of 50 W per unit length, and that the heat transfer due to surrounding air is only by natural convection. Determine the surface temperature of the cable when (a) in the summer time the air temperature is 35°C and (b) in the winter time the air temperature is 25°C.

Question

GIVEN

• Overhead heated electric transmission lines loosing heat due to convection

• Heat dissipation rate= 50 W/m

• Diameter of transmission lines (D) = 3 cm= 0.03 m

• Ambient air temperature during summer (T?)

At summer = 35°C At winter= 250C

FIND

(Surface temperature of cable in (a) Summer (b) Winter

SKETCH



ASSUMPTIONS

Air is still

Surface temperature is uniform and constant

Air properties are constant along the range of temperature.

PROPERTIES AND CONSTANTS

for dry air at the assumed mean temperature of 50°C

Thermal expansion coefficient (?) = 0.003095 1/K

Thermal conductivity (k) = 0.0272 W/(m K)

Kinematic viscosity (?) = 18.5 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

(a) The Grashof number is



Nusselt number for thin horizontal wire is given we have





Thus, heat loss per unit length by convection is given by



(a) For summer T? =350C

Thus the wire surface temperature is



(b) For winter T? =250C

Thus the wire surface temperature is