An electrical current of 700 a flows through a stainless steel cable having a diameter of 5 mm and an electri- cal resistance of 6 × 10−4 ω/m (i. e., per meter of cable length). the cable is in an environment having a tem- perature 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?