Heat transfer model for dropwise condensation on hydrophobic and superhydrophobic interfaces

Heat transfer models for condensation on hydrophobic and superhydrophobic interfaces are broadly available based on thermal resistance correlations. In the previous studies, very few models are presented based on the scaling factor or Nusselt number, and no model is available that directly correlates Biot number. This study develops a heat transfer model for dropwise condensation underneath a horizontal surface. The present model correlates with the Biot number to predict the heat transfer, temperature variation at the interfaces, solid-liquid, and liquid-vapor, and the growth rate of droplet condensate on the hydrophobic and superhydro-phobic interfaces by using Archimedes’ hat-box theorem. The present model is validated with analytical and experimental results against hydrophobic and superhydrophobic contact angles of similar working parameters made excellent agreements. The analytical model for dropwise condensation produces inaccurate results due to discrepancies and discontinuities due to mul-tiple correlations in the modeling. The present model is modified to obtain a continuous result using experimental data. The modified model is used for analyzing heat transfer by varying Biot numbers from 0.0001 to 1000 using Python 3.6.1 with an accuracy of 10-4. Simulation of the present model results in constant heat transfer at Bi = 4, irrespective of the contact angle. A negligible amount of coating resistance and interface resistance when Bi > 0.1, curvature effect when Bi > 0.04, droplet resistance when Bi < 0.02, the maximum liquid-vapor interface tem-perature at Bi ≈ 10, and maximum solid-liquid interface temperature at Bi ≈ 5, are presented.