Question

An aluminum transmission line with a diameter of 20 mm has an electrical resistance of R'elec=...

An aluminum transmission line with a diameter of 20 mm has an electrical resistance of R'elec= 2.636 × 10-4 Ω/m and carries a current of 700 A. The line is subjected to frequent and severe cross winds, increasing the probability of contact between adjacent lines, thereby causing sparks and creating a potential fire hazard for nearby vegetation. The remedy is to insulate the line, but with the adverse effect of increasing the conductor operating temperature.


(a) Calculate the conductor temperature when the air temperature is 0°C and the line is subjected to cross flow with a velocity of 20 m/s.

(b) Calculate the conductor temperature for the same conditions, but with a 2-mm-thick insulation having a thermal conductivity of 0.15 W/m · K.

Evaluate the properties of air at 300 K.

Step 1

What is the rate of heat loss by convection per unit length of the transission line, in W/m?

Step 2

What is the Nusselt number for the case without insulation?

Step 3

What is the line temperature for the case without insulation, in °C?

Step 4
What is the convection heat transfer coefficient for the case with a 2-mm-thick insulation having a thermal conductivity of 0.15 W/m·K, in W/m2·K?

Step 5
What is the total thermal resistance per unit length for the case with insulation, in K·m/W?

Step 6
What is the line temperature for the case with insulation, in °C?

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