Effect of interface curvature on isothermal heat transfer in a hydrophobic microchannel with transverse ribs and cavities

Abstract

Superhydrophobic microchannels have been found to deliver remarkable frictional flow resistance reduction owing to entrapped air on its surface micro texture. However, the entrapped air may adversely affect the heat transfer performance of the channel due to the increased thermal resistance offered by air. Hence the suitability of superhydrophobic microchannels in micro-scale heat transfer applications can only be ascertained through a combined thermo-hydraulic performance analysis which provides the trade-off between the decreased frictional resistance and increased thermal resistance. In this work, the thermo-hydraulic performance of a superhydrophobic microchannel consisting of transverse ribs and cavities is numerically investigated, at isothermal wall conditions, using CFD software Ansys-Fluent. The ribs and cavities that make up the channel wall can be represented by alternate no-slip (isothermal rib) and shear-free (adiabatic meniscus) zones. The liquid-gas interface formed at the cavity that separates the core flow and entrapped air forms convex, flat or concave menisci depending on the Laplace pressure. The effect of menisci shape on the combined thermo-hydraulic performance is studied for different gas-fractions and protrusion angles. The Nusselt number (Nu), Poiseuille number (fRe) and its ratio (Nu/fRe), are estimated for each case under convective heat transport settings. Increased shear-free fraction leads to an increase in the thermo-hydraulic performance. The concave menisci exhibited a uniform Nu irrespective of the protrusion angle, since the liquid near the interface is almost stagnant between successive no-slip riblets. In contrast, the convex interface demonstrated a drop in Nu with the rise in protrusion angle. The ribbed hydrophobic channel exhibited better performance than a no-slip classical channel having uniform heating for a protrusion angle range of -20°<0<+20° at different shear-free fractions. Moreover, the maximum thermo-hydraulic performance is observed for a nearly flat profile, which is in-line with the previous experimental observations. The thermal boundary layer development over the ribs and cavities is found to significantly influence the assessment of Nu and consequently the typical usage of a periodic boundary condition induces appreciable error in Nu estimation. For instance, a hydrophobic microchannel formed with 20 repeating units of ribs and cavities exhibited an error of 27% in Nu estimation in comparison with the asymptotic Nu, at a moderate Reynolds number of 100. Furthermore, two-phase VOF simulations are performed to compare the heat transfer characteristics of ribbed channels with and without the presence of entrapped air inside the cavities. Finally, the suitability of shear-free and adiabatic conditions is underscored through multi-phase simulations.