Temperature Jump Coefficient for Superhydrophobic Surfaces

Abstract

Mathematical models are developed for heat conduction in creeping flow of a liquid over a microstructured superhydrophobic surface, where because of hydrophobicity, a gas is trapped in the cavities of the microstructure. As gas is much lower in thermal conductivity than liquid, an interfacial temperature slip between the liquid and the surface will develop on the macroscale. In this note, the temperature jump coefficient is numerically determined for several types of superhydrophobic surfaces: a surface with parallel grooves, and surfaces with two-dimensionally distributed patches corresponding to the top of circular or square posts, and circular or square holes. These temperature jump coefficients are found to have a nearly constant ratio with the corresponding velocity slip lengths.