### Abstract

A simple model of evaporation from warm pools of water with turbulent, natural convection flow in the vapor phase is presented. The model is applicable from the dilute, low mass-transfer rate regime (room temperature) through the high mass-transfer rate regime (up to 99 °C). The model is applied to spent-fuel pool (SFP) heat and mass transfer during emergency conditions (e.g., plant blackout), and, in particular, to Fukushima. Comparisons with previous models are made. A simple analytic formula is presented that is nearly explicit in solving for pool temperature. The formula separates the more temperature-dependent properties from less temperature-dependent ones via a non-dimensional ratio Q_{u} = q_{u}/q_{u,b}, where q_{u} is the arbitrary (but specified) evaporative (latent) heat flux (∼decay heat for SFP) and q_{u,b} is the latent heat flux characteristic of incipient boiling. The latter has a simple, relatively temperature-independent expression, q_{u,b} = (h_{fg} Le^{2/3} h^{*})/C_{p}, where h^{*} is the dilute-limit heat transfer coefficient. This formula predicts that for natural convection at 99 °C (h^{*} ∼ 10 W/m^{2} K) q_{u,b} is approximately 18 kW/m^{2}, slightly greater than, but of the same order of magnitude as, pool boiling heat flux at the onset of nucleate boiling. A new blowing factor correlation is presented for high-rate mass-transfer (B_{m} > 1) of air–water vapor (Pr ∼ 0.7, Sc ∼ 0.6) turbulent natural convection flow over a heated horizontal surface for pool temperatures up to 99 °C (incipient boiling).

Original language | English (US) |
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Pages (from-to) | 703-714 |

Number of pages | 12 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 116 |

DOIs | |

State | Published - Jan 1 2018 |

### Keywords

- Mass transfer
- Natural convection
- Spent-fuel pool

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes