Question 10.25: KNOWN: Small copper sphere, initially at a uniform temperatu......
KNOWN: Small copper sphere, initially at a uniform temperature, \mathrm T_{\mathrm i}, greater than that corresponding to the Leidenfrost point, \mathrm T_{\mathrm D}, suddenly immersed in a large fluid bath maintained at \mathrm T_{\text{sat}}.
FIND: (a) Sketch the temperature-time history, T(t), during the quenching process; indicate temperature corresponding to \mathrm T_{\mathrm i}, \mathrm T_{\mathrm D}, \text{and}~\mathrm T_{\text{sat}}, identify regimes of film, transition and nucleate boiling and the single-phase convection regime; identify key features; and (b) Identify times(s) in this quenching process when you expect the surface temperature of the sphere to deviate most from its center temperature.
SCHEMATIC:
ANALYSIS: (a) In the right-hand schematic above, the quench process is shown on the “boiling curve” similar to Figure 10.4. Beginning at an initial temperature, \mathrm T_{\mathrm i} > \mathrm T_{\mathrm D}, the process proceeds as indicated by the arrows: film regime from i to D, transition regime from D to C, nucleate regime from C to A, and single-phase (free convection) from A to the condition when \Delta\mathrm T_{\mathrm e} = \mathrm T_{\mathrm s} – \mathrm T_{\text{sat}} = 0. The quench process is shown on the temperature-time plot below and the boiling regimes and key temperatures are labeled..
The highest temperature-time change should occur in the nucleate pool boiling regime, especially near the critical flux condition, \mathrm T_{\mathrm c}. The lowest temperature-time change will occur in the single-phase, free convection regime.
(b) The difference between the center and surface temperature will occur when \mathrm{Bi} = \mathrm{hr}_{\mathrm o}/3\mathrm k ≥ 0.1. This could occur in regimes with the highest convection coefficients. For example, h = 10,000 W/m² ·K which might be the case for water in the nucleate boiling regime, C-A, Bi ≈ 10,000 W/m² (0.010 m)/3 × 400 W/m·K = 0.08. For a sphere of larger dimension, in the nucleate and film pool boiling regimes, we could expect temperature differences between the center and surface temperatures since Bi might be greater than 0.1.
