A mathematic model for predicting the volume of water bridge retaining between vertical fin surfaces

• A mathematical model of water bridge volume was developed for predicting drainage performance.
• The four-degree polynomial was proposed to describe the meniscus curve of water bridge.
• The visual experimental setup for observing the front and side shapes of water bridge was built.
• The contours and volumes of water bridges predicted by the model agree well with the experiment.

As the volume of water bridge retaining between vertical fins affects the discharge of water bridge from the fin-and-tube heat exchangers, a mathematical model for predicting the volume of water bridge was developed in this study. In the model, the water bridge volume is calculated by the integral of the meniscus curve along the triple contact line; the triple contact line on the water–fin interface is described by the ellipse function; the meniscus curve on the water–air interface is described by a four-degree polynomial correlated based on the analytical solution of the Young–Laplace equation. The visual experiments were performed to validate the proposed model. It is shown that the predicted shapes of water bridges can qualitatively agree with the visualization images; the predicted volumes of water bridges can decribe 86% of the experimental data within the deviation limit of ±15% and the mean deviation is 10.5%.