An aluminum transmission line with a diameter of \(20 \mathrm{~mm}\) has an electrical resistance of \(R_{\text {elec }}^{\prime}=\) \(2.636 \times 10^{-4} \Omega / \mathrm{m}\) and carries a current of \(700 \mathrm{~A}\). 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 \(20^{\circ} \mathrm{C}\) and the line is subjected to cross flow with a velocity of \(10 \mathrm{~m} / \mathrm{s}\).

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

(c) Calculate and plot the temperatures of the bare and insulated conductors for wind velocities in the range from 2 to \(20 \mathrm{~m} / \mathrm{s}\). Comment on features of the curves and the effect of the wind velocity on the conductor temperatures.