Reference no: EM132641080

A long metallic wire is covered by electrical insulation. The insulation has an inner radius RI, i , and outer radius RI, o and a thermal conductivity of ki. The wire is operated in ambient air at T∞ and produces a power P' per unit length of wire. The convective heat transfer coefficient is h.

To sum up, assume known all needed thermal properties, the dimensions associated with the wire and the insulation, the convective heat transfer coefficient, the ambient temperature and the power per unit length produced by the metallic.

1) Find temperature the temperature as a function of radius in the metallic wire, starting from heat diffusion equation and the appropriate boundary conditions. In what aspect the heat conduction equation differs when applied to the wire and to the insulation layer domains?

2) Sketch the temperature variation in the metallic wire as function of the radius from the center of the wire to the surface of the wire in contact with the insulation RI, i. What can you tell about the temperature slope on each side of the wire/insulation interface? (Assume no contact resistance between the wire and the insulation).

3) Based on the above derived temperature function, determine the heat transfer rate in the wire at r=0 and r=RI,i. Why is the heat transfer rate changing with position inside the wire, but not inside the insulation?

4) What is the heat flux in the wire at r=0 and r=RI,I? What are the factors that contribute to the change in heat flux with position in this case? What are the factors that result in a changing heat flux in the insulation layer?