A long power transmission cable is buried at a depth (ground-to-cable-centerline distance) of 2 m. The cable is encased in a thin-walled pipe of 0.1-m diameter, and, to render the cable superconducting (with essentially zero power dissipation), the space between the cable and pipe is filled with liquid nitrogen at 77 K. If the pipe is covered with a super insulator (ki = 0.005 W/mK) of 0.05-m thickness and the surface of the earth (kg = 1.2 W/mK) is at 300 K, what is the cooling load (W/m) that must be maintained by a cryogenic refrigerator per unit pipe length?

Explanation:

From the question we are told that:

Ground-to-cable-center line Distance

Diameter of Cable case

Temperature of Nitrogen

Insulator

Thickness

Mass

Temperature of earth surface

Generally the equation for Heat rate per unit length is mathematically given by

Where

And

Therefore

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