Question

A 2-mm-diameter electrical wire is insulated by a 2-mm-thick rubberized sheath (k = 0.13 W/m K), and the wire/sheath interface is characterized by a thermal contact resistance of R"t,c= 3x10-4 m2 K/W. The convection heat transfer coefficient at the outer surface of the sheath is 10 W/m2 K, and the temperature of the ambient air is 20o C. If the temperature of the insulation may not exceed 50o C, what is the maximum allowable electrical power that may be dissipated per unit length of the conductor? What is the critical radius of the insulation?

Answer 1

Answer:

maximum allowable electrical power=4.51W/m

critical radius of the insulation=13mm

Explanation:

Hello!

To solve this heat transfer problem we must initially draw the wire and interpret the whole problem (see attached image)

Subsequently, consider the heat transfer equation from the internal part of the tube to the external air, taking into account the resistance by convection, and  conduction as shown in the attached image

to find the critical insulation radius we must divide the conductivity of the material by the external convective coefficient

$r=\frac{k}{h} =\frac{0.13}{10}=0.013m=13mm$