Simulation of flow and heat transfer in a liquid drop sliding underneath a hydrophobic surface

Wall shear stress and local heat fluxes have been determined in the present work by solving the Navier-Stokes and energy equations in three-dimensions on an unstructured tetrahedral grid that represents an individual droplet. The drop size and relative velocity are parameterized by the Reynolds number (Re = 10-1000), apparent contact angle (90-120°) and its shape. The simulations presented here are for a wide range of Prandtl numbers, i.e., 0.005-30. The wall shear stress and wall heat flux are expressed in terms of the skin friction coefficient and the Nusselt number, respectively. While these two quantities show an increase with Reynolds number, they decrease at higher values of the drop contact angle on/underneath hydrophobic surface. At low Prandtl numbers, heat transfer is mainly diffusional and the wall Nusselt number is practically independent of Reynolds number at any given Pr. The maximum wall shear stress as well as heat flux occurs at the corners of the drop close of the three-phase contact line. The surface averaged shear stress and heat flux are expressed in terms of appropriate correlations that include Reynolds number, Prandtl number, and the apparent contact angle. The wall shear stress in the relatively inactive central region at the drop base is smaller than the overall base average by a factor of 6, while that for heat transfer, the corresponding factor is in the range of 1.3-1.8. The figure of merit function, represented by the ratio of average Nusselt number to the friction coefficient, increases with contact angle, indicating an advantage to be gained from hydrophobic surfaces. The information presented in this paper is vital for further improvement of the available models of dropwise condensation on textured surfaces.