Hydrodynamic slip, the motion of a liquid along a solid surface, represents a fundamental phenomenon in fluid dynamics that governs liquid transport at small scales. For polymeric liquids, de Gennes predicted that the Navier boundary condition together with polymer reptation implies extraordinarily large interfacial slip for entangled polymer melts on ideal surfaces; this Navier-de Gennes model was confirmed using dewetting experiments on ultra-smooth, low-energy substrates. Here, we use capillary leveling—surface tension driven flow of films with initially non-uniform thickness—of polymeric films on these same substrates. Measurement of the slip length from a robust one parameter fit to a lubrication model is achieved. We show that at the low shear rates involved in leveling experiments as compared to dewetting ones, the employed substrates can no longer be considered ideal. The data is instead consistent with a model that includes physical adsorption of polymer chains at the solid/liquid interface.
The present numerical investigation aims to analysis the enhancement heat transfer in the nanofluid filled-complex geometries saturated with a partially layered porous medium. The vertical walls of the cavity are taken as complex wavy geometries. The horizontal walls of the cavity are flat with insulated temperature. The complex wavy cavity is filled with a nanofluid and the upper half of the wavy cavity is saturated with the porous medium. In the analysis, the governing equations are formulated for natural convection under the Boussinesq approximation in various environments including pure-fluid, nanofluid, and porous medium. In this investigation, the effects of the Rayleigh number (10 3 ≤ ≤ 10 5), Darcy parameter (10 −6 ≤ ≤ 10 −3), thermophoresis parameter (0.1 ≤ ≤ 0.5), nanofluid buoyancy ratio (0.1 ≤ ≤ 0.5), Brownian motion parameter (0.1 ≤ ≤ 0.5), inclination angle (0 0 ≤ ≤ 90 0), and geometry parameters 1 and have been studied on the streamlines, temperature, nanoparticles volume fraction, local Nusselt number and the local Sherwood number ℎ. It is found that, the performance of the heat transfer can be improved by adjusting the geometry parameters of the wavy surface. Overall, the results showed that the nanofluid parameters enhance the convection heat transfer and the obtained results provide a useful insight for enhancing heat transfer in two separate layers of nanofluid and porous medium inside complex-wavy cavity.
In this paper, we introduced a numerical analysis for the effect of a magnetic field on the mixed convection and heat transfer inside a two-sided lid-driven cavity with convective boundary conditions on its adjacent walls under the effects of the presence of thermal dispersion and partial slip. A single-phase model in which the water is the base fluid and a copper is nanoparticles is assumed to represent the nanofluid. The bottom and top walls of the cavity move in the horizontal direction with constant speed, while the vertical walls of the cavity are stationary. The right wall is mentioned at relatively low temperature and the top wall is thermally insulated. Convective boundary conditions are imposed to the left and bottom walls of the cavity and the thermal dispersion effects are considered. The finite volume method is used to solve the governing equations and comparisons with previously published results are performed. It is observed that the increase in the Hartmann number causes that the shear friction near the moving walls is enhanced and consequently the horizontal velocity component decreases.
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