This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) wails. The superhydrophobic waiis considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie-Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative moduie width) also influences the Nusselt number. The spatially varying Nusseit number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0-0.99 and 0.01-1.0, respectively. From these results, the ribicavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusseit number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightfoiward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

Accurate models for condensation heat transfer are necessary to improve condenser design. Drop-size distribution is an important aspect of heat transfer modeling that is difficult to measure for small drop sizes. The present work uses a numerical simulation of condensation which incorporates the possibility of coalescence and coalescenceinduced jumping over a range of drop sizes. Results of the simulation are compared with previous theoretical models and the impact of the assumptions used in those models is explored. In particular, previous drop-size distribution models may predict heat transfer rates less accurately for high contact angles and for coalescence-induced jumping since coalescence occurs over a range of drop sizes and does not always result in departure. The influence of various input parameters (nucleation site distribution approach, nucleation site density, contact angle, maximum drop size, heat transfer modeling to individual drops, and minimum jumping size) on the drop-size distribution and overall heat transfer rate is explored. Assignment of the nucleation site spatial distribution and heat transfer model affect both the drop-size distribution and predicted overall heat transfer rate. Results from the simulation suggest that, when the contact angle is large (as on superhydrophobic surfaces) and no coalescence-induced jumping occurs, the heat transfer may not be as sensitive to the maximum drop-size as previously supposed. Furthermore, this work suggests that when coalescenceinduced jumping occurs, reducing the maximum drop size may not always increase heat transfer since drops similar in size to those removed by coalescence-induced jumping can contribute significantly to the overall heat transfer rate.

This paper explores the influence surface slip, uniform in all directions with constant slip length, exerts on the physics of laminar jet impingement on a flat horizontal surface. Slip exists on superhydrophobic surfaces, and due to the relatively thin film dynamics associated with the growth of the laminar jet after impingement, its influence on the fluid physics is significant. An analysis based on momentum considerations is presented that allows prediction of the relevant thin film parameters as a function of radial position from the impingement point, jet Reynolds number, and constant relative slip length of the surface. Further, the analysis allows determination of the hydraulic jump location in terms of laminar jet characteristics and imposed downstream liquid depth. The results reveal that at a given radial location, the boundary layer growth and thin film thickness decrease, while the surface velocity of the thin film increases with increasing slip at the surface. The departure from classical no-slip behavior is quantified over a range of realizable slip conditions. Increasing slip length also leads to formation of hydraulic jumps at increasing radial location. An expression based on the results is presented that allows prediction of the hydraulic jump location as a function of the magnitude of the slip and all other influencing variables.

This paper presents an analytical investigation of the thermal transport in a parallel-plate channel comprised of superhydrophobic walls. An analytical solution is obtained for the thermally developing state, however, it is the condition far downstream from the entrance where the temperature field exhibits repeating periodic streamwise variation that is of primary interest here. The superhydrophobic walls considered in this paper exhibit alternating microribs and cavities positioned perpendicular to the flow direction and the transport scenario analyzed is that of constant wall heat flux through the rib surfaces with negligible thermal transport through the vapor cavity interface. Axial conduction is neglected in the analysis and the problem is one of Graetz flow with apparent slip-flow and periodicity of constant heating. Closed form solutions for the local Nusselt number and wall temperature are presented and are in the form of infinite series expansions. Previously, it has been shown that significant reductions in the overall frictional pressure drop can be expected relative to the classical smooth channel laminar flow. The present results reveal that the overall thermal transport is markedly influenced by the relative cavity region (cavity fraction), the relative rib/cavity module width, and the flow Peclet number. The following conclusions can be made regarding thermal transport for a constant heat flux channel exhibiting the superhydrophobic surfaces considered: (1) Increases in the cavity fraction lead to decreases in the average Nusselt number; (2) Increasing the relative rib/cavity module length yields a decrease in the average Nusselt number; and (3) as the Peclet number increases the average Nusselt number increases. For all parameters explored, the limiting upper bound on the fully developed average Nusselt number corresponds to the limiting case scenario of classical laminar flow through a smooth-walled channel with constant heat flux.

This work presents on the hydrodynamics of water droplet impingement on superheated solid surfaces across the entire wettability spectrum: superhydrophilic, hydrophilic, hydrophobic and superhydrophobic. While a large body of work exists on droplet impingement on hydrophilic and superhydrophilic surfaces, impingement on the latter two has been largely neglected and the present results show that dynamics are dramatically different. Experiments ranging in surface temperature from 125 • C to 415 • C and Weber numbers from 10 to 225 were performed and analyzed using high-speed imaging. Some of the most striking differences are as follows. While atomization is always present for impingement on the hydrophilic and superhydrophilic surfaces at temperatures below the Leidenfrost point, atomization is absent at low Weber numbers and at low excess surface temperatures on the hydrophobic surface. At high surface temperatures, the attraction of vapor bubbles on the hydrophobic surface allows a vapor blanket to form more readily thus leading to Leidenfrost behavior at a much lower temperature than classically observed on a hydrophilic surface. One of the most interesting phenomenon that will be discussed includes what will be described as a "pseudo-Leidenfrost" state for impingement on the superhydrophobic surface. Because water can be suspended at the peaks of the roughness on a superhydrophobic interface, vapor escapes from underneath the droplet thus mimicking Leidenfrost behavior for all excess temperatures. This results in minimal atomization for superhydrophobic impingement over the entire regime explored. Finally, maximum spread diameters for Leidenfrost impingement are tabulated as a function of the Weber number for all surfaces and are shown to be larger on the smooth surfaces than on the textured ones indicating that droplet spreading at the Leidenfrost point is not independent