Known: initial temperature, thickness and thermal diffusivity of glass plate. Find: (a) time to achieve 50% reduction in midplane temperature, (b) maximum temperature gradient at that time. Analysis: prescribed surface temperature is analogous to h and t = ts. Assume validity of one-term approximation to series solution for t (x,t). (a) at the midplane, Comments: validity of one-term approximation is confirmed by fo > 0. 2. Known: steel ball bearings at an initial, uniform temperature are to be cooled by convection while passing through a refrigerated chamber; bearings are to be cooled to a temperature such that 70% of the thermal energy is removed. Find: residence time of the balls in the 5 m-long chamber and recommended drive velocity for the conveyor. Assumptions: (1) negligible conduction between ball and conveyor surface, (2) negligible radiation exchange with surroundings, (3) constant properties, (4) uniform convection coefficient over ball"s surface. Analysis: the biot number for the lumped capacitance analysis is.