Effective temperature jump length and influence of axial conduction for thermal transport in superhydrophobic channels

This paper presents a numerical investigation of thermal transport in a parallel-plate channel comprised of superhydrophobic walls. The scenario analyzed is laminar, fully developed, steady flow with constant properties. The superhydrophobic walls considered here have alternating micro-ribs and cavities aligned perpendicular to the flow direction and are made of a highly conductive material. The cavities are assumed to be non-wetting and contain air whereas the bulk liquid is water. The thermal transport through the ribs is considered to have a constant heat flux while the thermal transport through the air/liquid interface over the cavity is considered to be negligible. Numerical results have been obtained for a range a Peclet numbers, cavity fractions, and relative channel widths. A limited number of results were also obtained where the rib was maintained at a constant temperature condition for comparison. In general, the thermal transport is a strong function of all the parameters explored. By comparison to previous analytical work, the influence of axial conduction is found to be significant and is most pronounced at large relative channel widths, low Peclet numbers, and large cavity fractions. Lastly, the ratio of temperature jump length to hydrodynamic slip length is presented in terms of the varied parameters and is compared to previous results where axial conduction is neglected and other work where diffusion is assumed dominant.