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/m^2K.
(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 m^2 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?