A small copper sphere, initially at a uniform, elevated temperature T(0) = T;, is suddenly immersed in a large fluid bath maintained at Tsat. The initial temperature of the sphere exceeds the Leiden frost point corresponding to the temperature TD of Figure 10.4.

(a) Sketch the variation of the average sphere temperature, T(t), with time during the quenching process. Indicate on this sketch the temperatures Ti, TD, and Tsat as well as the regimes of film, transition, and nucleate boiling and the regime of single-phase convection. Identify key features of the temperature history.

(b) At what time(s) in this cooling process do you expect the surface temperature of the sphere to deviate most from its center temperature? Explain your answer.