Chapter 8, Problem 8.91P

To slow down large prime movers like locomotives, a process termed dynamic electric braking is used to switch the traction motor to a generator mode in which mechanical power from the drive wheels is absorbed and used to generate electrical current. As shown in the schematic, the electric power is passed through a resistor grid (a), which consists of an array of metallic blades electrically connected in series (b). The blade material is a high-temperature, high electrical resistivity alloy, and the electrical power is dissipaled as heat by internal volumetric generation. To cool the blades, a motor-fan moves high-velocity air through the grid.

(a) Treating the space between the blades as a rectangular channel of $\text{22}0-\text{mm}\times \text{4}-\text{mm}$ cross section and $\text{7}0-\text{mm}$ length. estimate the heat removal rate per blade if the airstream has an inlet temperature and velocity of $\text{25}°\text{C}$ and $\text{5}0\text{ m}/\text{s}$ . respectively. while the blade has an operating temperature of $\text{6}00°\text{C}$ .

(b) On a locomotive pulling a 10-car train, there may be 2000 of these blades. Based on your result from part (a), how long will it take to slow a train whose total mass is $\text{1}0\text{6 kg}$ from a speed of $\text{12}0\text{ km}/\text{h}$ to $\text{5}0\text{ km}/\text{h}$ using dynamic electric braking?