Question

In an industrial process, 20 mm diameter spherical steel ball bearings are heat-treated to improve their durability. For application (1), the entire ball bearing needs to be heated evenly to 1000 K. For application (2), only the outer 1 mm of the ball is to be heated to a temperature in excess of 1000 K. The properties of the ball bearing are c = 0.5 kJ/kg*K; p = 7800 kg/m³; k = 50 W/m.K. At your facility, you have access to two heating processes: a high-temperature convection oven (Tmax = 1200 K) and a liquid-salt immersion bath (Tmax = 1200 K). The convective heat transfer coefficients (h) are 50 W/m²K for the oven and 5000 W/m²K for the bath.

a) Which process would you use for each application, and why?

b) For application (1), using the process you selected in (a) calculate the time required to heat a ball that starts from 50^oC to the target temperature of 1000 K.

c) For application (2), using the process you selected in (a), calculate the time required to heat the outer layer of the ball to its target temperature.

d) For your answer in (c), what would be the temperature at the centre of the ball?

Answer 1