Thermal resistance of heated superhydrophobic channels with streamwise thermocapillary stress

A pressure-driven channel flow between a longitudinally-ridged superhydrophobic surface (SHS) and solid wall is studied, where a constant heat flux enters the channel from either the SHS or solid wall. First, a model is developed which neglects thermocapillary stresses (TCS) in the transverse direction. The caloric, convective and total thermal resistance are evaluated and their dependence on the shape of the liquid–gas interface (meniscus), gas ridge width, texture period, channel height, streamwise TCS, Péclet number and channel length is established. The caloric resistance is minimised with menisci that protrude into the gas cavity, large slip fractions, small channel heights and small streamwise TCSs. When heating from the SHS, the convective resistance increases, and therefore, a design compromise exists between caloric and convective resistances. However, when heating from the solid wall, the convective resistance remains the same and SHSs that minimise caloric resistance are optimal. We investigate both water and Galinstan for microchannel applications and find that both configurations can have a lower total thermal resistance than a smooth-walled channel. Heating from the solid wall is shown to always have the lowest total thermal resistance. Numerical simulations are used to analyse the effect of transverse TCSs. Our model captures much of the physics in heated superhydrophobic channels, but is computationally inexpensive when compared to the numerical simulations.