A cold air chamber is proposed for quenching steel ball bearings of diameter D = 0.2 m and initial temperature T_i = 400°C. Air in the chamber is maintained at – 15°C by a refrigeration system, and the steel bans pass through the chamber on a conveyor belt. Optimum bearing production requires that 70% of the initial thermal energy content of the ban above - 15°C be removed. Radiation effects may be neglected, and the convection heat transfer coefficient within the chamber is 1000 W/m² ∙ K. Estimate the residence time of the balls within the chamber, and recommends a drive velocity of the conveyor. The following properties may be used for the steel: k = 50 W/m ∙ K, a = 2 X 10^-5 m²/s, and

c = 450 J/kg ∙ K.

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5 m Ball Chamber housing bearing Cold air Belt