Chapter 1, Problem 1.84P

Bus bars proposed for use in a power transmission station have a rectangular cross section of height $H=600\text{mm}$ and width $W=200\text{mm}\text{.}$ The electrical resistivity, ${\rho }_e\left(\mu \Omega \cdot \text{m}\right),$ of the bar material is a function of temperature, where ${\rho }_{e,o}=0.0828,\mu \Omega \cdot \text{m,}{T}_o=25°\text{C,}$ and $\alpha =0.0040{\text{K}}^{-1}.$ The emissivity of the bar’s painted surface is 0.8, and the temperature of the surroundings is $30°\text{C}$. The convection coefficient between the bar and the ambient air at $30°\text{C}$ is $10{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Assuming the bar has a uniform temperature T, calculate the steady-state temperature when a current of 60,000 A passes through the bar.
2. Compute and plot the steady-state temperature of the bar as a function of the convection coefficient for $10\le h\le 100{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ What minimum convection coefficient is required to maintain a safe-operating temperature below $120°\text{C?}$ Will increasing the emissivity significantly affect this result?