Improved modeling and correlation for heat transfer through a condensate droplet

In dropwise condensation, the heat transfer performance is determined by the heat transfer through a single droplet and the droplet size distribution on the cooled condensing surface. The conduction resistance inside a droplet is an important part of all heat transfer resistances, and it also affects the size distribution of small droplets further, such as in the popular population balance model. The heat transfer of a single droplet can be measured by the Nusselt number (Nu), and internal conduction resistance can be measured by the dimensionless shape factor (f). Previous studies have shown that Nu and f are functions of droplet contact angle (θ) and Biot number (Bi). Based on this, some fitting correlations of Nu or f in a certain range of Bi and θ are established. However, previous results show unreasonable values when Bi is very large or very small, the effective ranges of these fitting correlations are not broad enough, and the fitting accuracy is not gratifying enough. In this paper, the heat transfer characteristics of condensing droplets are investigated by a CFD method which is validated by comparing the simulation results and theoretical solution for hemisphere droplets. By adopting this method, f and Nu are obtained for droplets with 10° ≤θ≤ 170° and 10−3 ≤Bi ≤ 104. Considering the relationship between current numerical results and the model of Kim and Kim (2011), an improved general fitting correlation covering all 374 simulation cases is proposed, and the root mean square (RMS) errors of f and Nu are 3.6% and 2.6%, respectively