An electric current of 1 A passing through a cable has a measured voltage of 30 V across the cable. The cable is covered with polyethylene insulation, and convection occurs at the outer surface of the insulation. The ambient temperature is 20°C with a convection heat transfer coefficient of 5 W/m2•K, and the surface area subjected to the convection is 0.1 m2. The ASTM D1351 standard specifies that thermoplastic polyethylene insulation is suitable for use on electrical cable with operation at temperatures up to 75°C. Under these conditions, will the polyethylene insulation for the cable meet the ASTM D1351 standard? If the polyethylene insulation does not meet the ASTM D1351 standard, then discuss possible solutions to meet the standard.

Question

What will be an ideal response?

Answer 1

An electrical cable is covered with polyethylene insulation and is subjected to convection with the ambient air. Determine whether the insulation surface temperature meets the ASTM D1351 standard for polyethylene insulation.

Assumptions1 Steady operating conditions. 2 Radiation heat transfer is negligible. 3 No hot spot exists on the cable.

AnalysisThe electrical energy that is converted to thermal energy is determined using the Joule heating relation:

Q = IV = (1 A)(30 V) = 30 W

The thermal energy for the joule heating is then transferred through the insulation layer by conduction, and then by convection at the outer surface of the insulation. From the Newton’s law of cooling for convection, we have



Rearranging the equation and solving for the surface temperature,



Discussion With the surface temperature being 5°C higher than the specification of the ASTM D1351 standard for polyethylene insulation that means the temperature at the inner surface of the insulation being in contact with the cable would be higher than 80°C. To solve this problem, we will need to use a larger diameter (or thicker) cable. The electrical resistance decreases with increasing cable thickness, which would reduce joule heating. We can also use a different insulation material with a higher temperature rating. From the ASTM database, the crosslinked polyethylene insulation (ASTM D2655) is rated up to 90°C for normal operation.