Chapter 10, Problem 10.27P

A small copper sphere, initially at a uniform, elevated temperature $T\left(0\right)=T_i$ , is suddenly immersed in a large fluid bath maintained at $T_{\text{sat}}$ . The initial temperature of the sphere exceeds the Leidenfrost point corresponding to the temperature $T_D$ of Figure 10.4.

(a) Sketch the variation of the average sphere temperature, $\bar{T}\left(t\right)$ , with time during the quenching process. Indicate on this sketch the temperatures $T_i,T_D$ , and $T_{\text{sat}}$ 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.