Thermal transport due to buoyant flow past a vertical, heated superhydrophobic surface with uniform stream-wise slip

An analytical investigation of thermal transport due to laminar, buoyant flow past a vertical superhydrophobic (SHPo) surface was performed. The surface temperature is uniform and is greater than the temperature of the surrounding liquid. Uniform stream-wise hydrodynamic slip and temperature jump were imposed at the wall to model the SHPo surface. Applying an integral analysis within the boundary layer results in a system of differential equations, which was solved numerically to obtain boundary layer thickness and local and average values of the Nusselt number. The classical smooth hydrophobic scenario with no-slip and no temperature jump showed excellent agreement with previous analyses of the same problem. Solutions were obtained for laminar Rayleigh number ranging from 10(4) to 10(9) at a Prandtl number of 7. There was a modest decrease in the boundary layer thickness due to the increased slip length and the flow velocity decreased due to the increased temperature jump length. The local Nusselt number decreased as the temperature jump length increased, with greater reduction at larger Rayleigh numbers and near the lower edge. The decrease in the average Nusselt number relative to surfaces with no-slip and no temperature jump may be as much as 50%. (C) 2019 Elsevier Ltd. All rights reserved.