International Journal of Heat and Mass Transfer 151 (2020) 119413 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt Thermal modeling with diffusion for dropwise condensation of humid air Brian Frymyer, Nasser Vahedi, Sudhakar Neti, Alparslan Oztekin ∗ P.C. Rossin College of Engineering and Applied Science, Lehigh University, Bethlehem, PA 18015, United States a r t i c l e i n f o Article history: Received 7 July 2019 Revised 17 January 2020 Accepted 22 January 2020 1. Introduction Condensation is one of the most critical process in several in- dustries such as power generation, thermal management, water desalination and environmental control [1]. Typically, the vapor condenses on a surface due to the reduction in the energy barrier for nucleation. In conventional film condensation, the condensed vapor usually forms a thin liquid film on the surface resulting in film heat transfer. The thin film creates a large thermal resistance during steady-state heat transfer. Sustained dropwise condensation is an alternative to film condensation which maintains individual droplets on the surface. The rate of heat transfer can be increased by a factor of 5 to 7 times if dropwise condensation can be sus- tained [1,2]. The increased heat transfer associated with dropwise condensation is accomplished by maintaining individual droplets on the surface which are smaller in height than the film resulting in a lower thermal resistance of the system. Dropwise condensa- tion can reduce the required approach temperatures or reduce the size of the heat exchanger, or recover more evaporative losses such as the associated loss of wet cooling water drift. One of the first to present details about dropwise condensa- tion was for Schmidt, et al. [3] as early as the 1930s. Dropwise condensation heat transfer is of significant scientific importance because of the potentially larger heat transfer it offers when com- pared to what is possible with film-wise heat transfer. Recently dropwise condensation has had increased scientific interest due to the potential for water conservation particularly with respect to cooling tower drift, water purification, improved condenser performance, and desalinization [4–6]. The Namib Desert beetle harvests moisture from the air for survival by utilizing a combi- nation of hydrophilic and hydrophobic surfaces [7,8]. The potential ∗ Corresponding author. E-mail address: alo2@lehigh.edu (A. Oztekin). for creating a bio-mimic device based on the Namib Desert beetle has reinforced the view that water harvesting from humid air is a feasible solution. Models for heat transfer have been developed since the mid- 1960 ′ s using scaling to apply the heat transfer of an individual droplet where the scaling predicts the surface density of the droplets [9]. The scaling approximations assume a constant distri- bution of droplet size on the surface and based on the expected droplet size distribution and quantity of droplets. Several scaling approximations have been developed [10–15]. The scaling models attempt to predict the heat transfer rate based on expected surface coverage. These models are approximations of the heat transfer phenomenon and do not directly take into account the common occurrence of droplets rolling off the surface and creating a free area for new droplets to nucleate. The current models include sweeping rates [10] which are not an accurate representation of highly hydrophobic surfaces which result in almost continuous flow. These models do not directly take into account the nucle- ation rate of the surface, but use it to estimate the droplet density on the surface [10]. The removal of droplets from the surfaces has a significant impact on the heat transfer rate. Scaling models and the existing thermal models for heat transfer associated with an individual droplet do not include an equivalent thermal resistance due to diffusion. The lack of details provided in the scaling model requires performing experimental analysis to establish actual mass collection and drainage ratio. The only existing model comparable to the model presented here is a finite element type analysis that evaluated a couple of adjacent drops [16] and a model developed for moderately hydrophobic surfaces [17]. A more comprehensive model is required to allow optimization prior to experimentation such that the experiment confirms the expected optimization for the system [18]. A model for heat transfer of the individual droplet was devel- oped by Kim and Kim [10]. The model includes a thermal resis- tance associated with the liquid of the droplet, the capillary effect, https://doi.org/10.1016/j.ijheatmasstransfer.2020.119413 0017-9310/© 2020 Elsevier Ltd. All rights reserved.