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. Required:
a. Find temperature the temperature as a function of radius in the insulation, starting from heat diffusion equation and the appropriate boundary conditions.
b. Once you find the temperature as function of radius, determine the temperature gradient.
c. Sketch the temperature variation in the insulation layer as function of the radius from the inner surface