Inertial effects on thermal transport in superhydrophobic microchannels

This paper presents a numerical investigation on the effects of inertia for laminar fully developed flow in superhydrophobic microchannels where the surface structure consists of a square array of square pillars aligned with the flow direction. Infinite parallel plate channel flow is considered where the flow is assumed to be non-wetting and the meniscus is idealized as flat. A constant heat flux condition is imposed at the tops of the posts whereas the gas/liquid interface is assumed to be adiabatic. A wide range of Peclet numbers (1-10,000), relative channel spacing sizes (3 orders of magnitude), and solid fractions (0.02-0.9) are considered. The effect of these on friction factor-Reynolds number product, Nusselt number, hydrodynamic slip length and temperature jump length is explored. Frictional drag and convective heat transfer are reduced for all cases explored. These reductions are greater for small solid fractions, small relative channel sizes, and low Peclet numbers. Interestingly, over a wide range of explored parameters the results correspond well with the analytical diffusion dominated results present in the literature. It is only at the highest Peclet numbers and smallest relative channel sizes that the results deviate significantly from the diffusion dominated Stokes flow scenario. A mapping is presented that illustrates for which parameter ranges the influence of inertia and relative channel size become significant.