A Statistical Model of Bubble Coalescence and Its Application to Boiling Heat Flux Prediction—Part I: Model Development

In this work a statistical model is developed by deriving the probability density function $(pdf)$ of bubble coalescence on boiling surface to describe the distribution of vapor bubble radius. Combining this bubble coalescence model with other existing models in the literature that describe the dynamics of bubble motion and the mechanisms of heat transfer, the surface heat flux in subcooled nucleate boiling can be calculated. By decomposing the surface heat flux into various components due to different heat transfer mechanisms, including forced convection, transient conduction, and evaporation, the effect of the bubble motion is identified and quantified. Predictions of the surface heat flux are validated with R134a data measured in boiling experiments and water data available in the literature, with an overall good agreement observed. Results indicate that there exists a limit of surface heat flux due to the increased bubble coalescence and the reduced vapor bubble lift-off radius as the wall temperature increased. Further investigation confirms the consistency between this limit value and the experimentally measured critical heat flux (CHF), suggesting that a unified mechanistic modeling to predict both the surface heat flux and CHF is possible. In view of the success of this statistical modeling, the authors tend to propose the utilization of probabilistic formulation and stochastic analysis in future modeling attempts on subcooled nucleate boiling.