Chapter 1, Problem 1.35P

An electrical resistor is connected to a battery, as shown schematically. After a brief transient, the resistor assumes a nearly uniform, steady-state temperature of $95°\text{C,}$ while the battery and lead wires remain at the ambient temperature of $25°\text{C}\text{.}$ Neglect the electrical resistance of the lead wires.

1. Consider the resistor as a system about which a control surface is placed and Equation 1.12c is applied. Determine the corresponding values of ${\stackrel{.}{E}}_{in}\left(W\right),{\stackrel{.}{E}}_g\left(W\right),{\stackrel{.}{E}}_{out}\left(W\right),$ and ${\stackrel{.}{E}}_{st}\left(W\right).$ If a control surface is placed about the entire system, what are the values of ${\stackrel{.}{E}}_{in},{\stackrel{.}{E}}_g,{\stackrel{.}{E}}_{out},$ and ${\stackrel{.}{E}}_{st}?$
2. If electrical energy is dissipated uniformly within the resistor, which is a cylinder of diameter $D=60\text{mm}$ and length $L=250\text{mm,}$ what is the volumetric heat generation rate, $\stackrel{.}{q}\left({\text{W/m}}^{\text{3}}\right)?$ Neglecting radiation from the resistor, what is the convection coefficient?