An electrical current of 700 A flows through a stainless steel cable having a diameter of 5 mm and an electrical resistance of 6 X 10^-4 Ω/m (i.e., per meter of cable length). The cable is in an environment having a temperature of 30°C, and the total coefficient associated with convection and radiation between the cable and the environment is approximately 25 W/m² ∙ K.

(a) If the cable is bare, what is its surface temperature?

(b) If a very thin coating of electrical insulation is applied to the cable, with a contact resistance of 0.02 m² ∙ K/W, what are the insulation and cable surface temperatures?

(c) There is some concern about the ability of the insulation to withstand elevated temperatures. What thickness of this insulation (k = 0.5 W/m ∙ K) will yield the lowest value of the maximum insulation temperature? What is the value of the maximum temperature when the thickness is used?