No-slip Cases Research Articles

On the application of no-slip lateral boundary conditions to ‘coarsely’ resolved ocean models

The problem of no-slip boundary conditions as they apply to ocean models is revisited. It is argued that the setting is consistent with classical Law of the Wall theory. The rendering of no-slip boundary conditions is thus modified importantly from typical practice in ocean models. The proposed boundary condition formulation is implemented in the MITgcm. Comparisons with classically formulated free-slip and no-slip cases shows the results are somewhat between the two cases, but generally closer to free-slip.

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.

Modeling of Heat Transfer in Microchannel Gas Flow

Due to the existence of a velocity slip and temperature jump on the solid walls, the heat transfer in microchannels significantly differs from the one in the macroscale. In our research, we have focused on the pressure driven gas flows in a simple finite microchannel geometry, with an entrance and an outlet, for low Reynolds (Re<200) and low Knudsen (Kn<0.01) numbers. For such a regime, the slip induced phenomena are strongly connected with the viscous effects. As a result, heat transfer is also significantly altered. For the optimization of flow conditions, we have investigated various temperature gradient configurations, additionally changing Reynolds and Knudsen numbers. The entrance effects, slip flow, and temperature jump lead to complex relations between flow behavior and heat transfer. We have shown that slip effects are generally insignificant for flow behavior. However, two configuration setups (hot wall cold gas and cold wall hot gas) are affected by slip in distinguishably different ways. For the first one, which concerns turbomachinery, the mass flow rate can increase by about 1% in relation to the no-slip case, depending on the wall-gas temperature difference. Heat transfer is more significantly altered. The Nusselt number between slip and no-slip cases at the outlet of the microchannel is increased by about 10%.

Impact of slip and contact angle on imprinting pressure in nanoimprint lithography

Slip is well known to take place in micrometer- and nanometer-scale flows. In this study, slip and wall adhesion effects on the imprinting pressure of thermal nanoimprint lithography (NIL) were investigated using computational fluid dynamics. The influence of the mold pattern shape on the imprinting pressure was also analyzed. In thermal NIL, the importance of time in the filling process is relatively high. Reducing the imprinting pressure induces process speed increases, raising productivity a little. Full-slip and no-slip conditions were compared, and various contact angles were applied to survey the influence of the slip condition and wall adhesion, respectively. The full-slip cases required imprinting pressures less than the half values of the no-slip cases. The minimum imprinting pressure was required when the contact angle between the mold and polymer resist was 120°. It was confirmed that the residual thickness decreased as the amount of slip increased, leading to a diminution in the postprocessing time.

The combined effects of continents and the 660 km-depth endothermic phase boundary on the thermal regime in the mantle

We explore a wide range of parameter space to investigate the dynamical interaction between effects due to surface boundary conditions representing continental and oceanic lithosphere and the endothermic phase boundary at 660 km-depth in simple two-dimensional convection calculations. Phase boundary induced mantle layering is strongly affected by the wavelength of convective flows and mixed surface boundary conditions strongly increase the horizontal wavelength of convection. Our study shows that for mixed cases the effects of the surface boundary conditions dominate the effects of the phase boundary. We show that the calculations with complete continental coverage have the most significantly decoupled lower and upper mantle flows and substantial thermal and mechanical layering. Unlike the free-slip case where the surface heat flow decreases substantially with increasing magnitude of the Clapeyron slope, surface heat flow is shown to be almost independent of the Clapeyron slope for mixed boundary condition cases. Although very different when not layered, models with free and mixed surfaces have very similar planforms with very large aspect ratio flows when run with large magnitudes of the Clapeyron slope. We also calculate the critical boundary layer Rayleigh number as a measure of the thermal resistance of the surface boundary layer. Our results show that the thermal resistance in the oceanic and the continental regions of the mixed cases are similar to fully free and no-slip cases, respectively. We find that, even for purely basally heated models, the mantle becomes significantly subadiabatic in the presence of partial continental coverage. This is due to the significant horizontal advection of heat that occurs with very large aspect ratio convection cells.

The influence of slip on the peristaltic motion of a third order fluid in an asymmetric channel

In this investigation, the peristaltic flow of a third order fluid in an asymmetric channel is considered in the presence of a slip condition. The series solution of the stream function and longitudinal pressure gradient is given under long wave length and low Reynolds number approximations. Pressure rise and frictional forces per wave length are analyzed through numerical integration. Pumping and trapping phenomena are examined and the obtained results are compared with those of no-slip condition. Comparison is made with the results of no-slip and viscous fluid cases.

Peristaltic transport in a slip flow

Continuum-mechanic derivation of the entrainment of rarefied gases induced by a surface wave along walls (or peristaltic transport) in a confined parallel-plane microchannel is conducted by the perturbation method. Both no-slip and slip flow cases are investigated with the former ones matched with the previous approach by Fung and Yih. Critical reflux values due to first order slip-flow effects become trivial for the free pumping case, and decrease due to second order slip-flow effects after we compared them with no-slip cases.