Round cooper cable transmitting a current of 756 A has the d

Round cooper cable transmitting a current of 756 A has the diameter of 15.6 mm and electrical resistance of 10^-4 ohm/m. The cable is in cross flow of the wind which has the velocity of 6 m/s and temperature of -23 degree C (it is a winter:-)). Calculate the surface temperature and the centerline temperature of the cable. Please show all formulas and all steps of your derivations and calculations.

Solution

From electrical dissipation rate heat generated is I²R = 57.15 Watt ( J/s)

assume convective coeff h ( take from tables)

Q* Vol= h*DT*area

DT = Q*R/2h) = 57.15* (15.6/1000)/(2h)

hence surface temp known.

for centre line temp, assume KdT/Dr = heat flux ( linear approx)

find K for the material of cable. Heat flux is known so DT/Dr known

( for more exact use cyclindrical eqns which involve log r)