Chapter 3, Problem 3.53P

A wire of diameter $D=2\text{mm}$ and uniform temperatureT has an electrical resistance of $\text{0}\text{.01}\Omega /\text{m}$ and a currentflow of 20 A.

1. What is the rate at which heat is dissipated per unitlength of wire? What is the heat dissipation perunit volume within the wire?
2. If the wire is not insulated and is in ambient airand large surroundings for which $T_{\infty }=T_{\text{sur}}=20°\text{C,}$ what is the temperature T of the wire? Thewire has an emissivity of 0.3, and the coefficientassociated with heat transfer by natural convectionmay be approximated by an expression of theform, where $C=1.25{\text{W/m}}^{7/4}\cdot {\text{K}}^{\text{5/4}}.$ If the wire is coated with plastic insulation of 2-mmthickness and a thermal conductivity of $0.25W/m\cdot K,$ what are the inner and outer surface temperatures ofthe insulation? The insulation has an emissivity of0.9, and the convection coefficient is given by theexpression of part (b). Explore the effect of the insulationthickness on the surface temperatures.