Chapter 5, Problem 5.29P

A long wire of diameter $D=1\text{mm}$ is submerged in an oil bath of temperature $T_{\infty }=25°\text{C}\text{.}$ The wire has an electrical resistance per unit length of $R_e^{\text{'}}=0.01\Omega \text{/m}.$ If a current of $I=100\text{A}$ flows through the wire and the convection coefficient is $h=500{\text{W/m}}^{\text{2}}\cdot \text{K,}$ what is the steady-state temperature of the Wire? From the time the current is applied. how long does it take for the wire to reach a temperature that is within $1°\text{C}$ of the steady-state value? The properties of the wire are $\rho =8000{\text{kg/m}}^{\text{3}},c=500\text{J/kg}\cdot \text{K,}$ and $k=20\text{W/m}\cdot \text{K}\text{.}$