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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 balls pass through the chamber on a conveyor belt. Optimum bearing production requires that 70% of the initial thermal energy content of the ball above -15°C be removed. Radiation effects may be neglected, and the convection heat transfer coefficient within the chamber is 1000 W/m^{2} ∙ K. Estimate the residence time of the balls within the chamber, and recommend a drive velocity of the conveyor. The following properties may be used for the steel: and c = 450 J/kg ∙ K.
A soda lime glass sphere of diameter D1 25 mm is encased in a bakelite spherical shell of thickness L 10 mm. The composite sphere is initially at a uniform temperature, Ti = 40°C, and is exposed to a fluid at T_{∞} = 10°C with h = 30 W/m^{2} ∙ K. Determine the center temperature of the glass at t = 200 s. Neglect the thermal contact resistance at the interface between the two materials.
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