Chapter 4, Problem 145P

Stainless steel ball bearings $(p=8085{\text{ Kg/m}}^{\text{3}}\text{, k = 15}\text{.1 W/m}{\text{.}}^{\text{o}}\text{C, }{c}_p\text{ = 0}\text{.480 KJ/kg}{\text{.}}^{\text{o}}\text{C ,}$ and $\text{and }\alpha \text{ = 3}\text{.91 }\times {\text{ 10}}^{\text{-6}}{\text{m}}^{\text{2}}\text{/s)}$ having a diameter of 1.2 cm are to be quenched in water. The balls leave the oven at a uniform temperature of 900°C and are exposed to air at 30°C for a while before they are dropped into the water. If the temperature of the balls is not to fall below 850°C prior to quenching and the heat transfer coefficient in the air is 125 Wm² °C, determine how long they can stand in the air before being dropped into the water.