A fractal dropwise condensation heat transfer model including the effects of contact angle and drop size distribution

Abstract

In this paper, a new dropwise condensation heat transfer model is developed on the basis of Rose model for a drop heat transfer and random fractal functions for the drop size distributions of direct condensation drops and coalescence drops. Compared to the well-established Rose’s model, the new model considers the contact angle and its hysteresis, the nucleation site density, the fractal dimension for drop sizes and maximum and minimum drop radii. Expressions of the distributions functions for both the direct condensing drops and the coalescence drops are derived and calculated by introducing fractal theory, respectively. The total heat flux of dropwise condensation on the entire condensing surface is calculated as the sum of the contributions from the condensations of above mentioned two kinds of drops. The simulation results indicate that the fractal dimension for drop sizes distribution decreases with increase in contact angle, resulting in smaller departure diameters and even shorter life cycle, which plays an active role in higher heat transfer coefficients. But the decline of fractal dimension leads to the decrease in the number density of droplets, which has negative effects on heat transfer process. Attributing to the combined influences mentioned above, the maximum heat flux value is obtained at θ=135°. The model proposed is applicable to predict the heat flux of the condensing drops with a wide range of contact angles, and the prediction results can agree well with different experimental dropwise condensation heat transfer data obtained from experiments and majority of literature results by choosing the proper contact angle parameters. The study can also reasonably explain the cause of the diversities of the dropwise condensation heat transfer data from different references.