Problem $3(5$ points$)$: A solid wire of diameter $2$ mm and length $10$ m is wrapped along its length with a $1-$mm$-$thick plastic insulation cover of thermal

conductivity $0\mathrm{.}15\frac{W}{m}-K.$ Within the wire, volumetric energy generation rate is $0\mathrm{.}5M\frac{W}{m^3}.T_{}=30C$ and $h=25\frac{W}{m^2}K.$

Draw a neat schematic of the problem, showing relevant details

Determine the conduction heat transfer rate at the interface of the solid core and the insulation

Using thermal networks only, determine temperature at interface between solid core and insulation, and at end of the insulation

Sketch the temperature and heat flux profiles through the core and casing, and label nature of curves clearly

If thickness of the plastic cover is doubled, calculate temperature at interface between core and insulation