Newtonian fluids were placed between molecularly smooth surfaces whose spacing was vibrated at spacings where the fluid responded as a continuum. Hydrodynamic forces agreed with predictions from the no-slip boundary condition only provided that flow rate (peak velocity normalized by spacing) was low, but implied partial slip when it exceeded a critical level, different in different systems, cor...

In this paper, we use a lattice Boltzmann model (LBM) for simulation of rarefied gas flows in microchannels at high and moderate Knudsen numbers. The lattice Boltzmann method uses D2Q9 lattice structure and BGK collision operator with single relaxation time. The solid wall boundary conditions used in this paper are based on the idea of bounceback of the nonequilibrium part of particle distribut...

A Lattice Boltzmann method is applied to demonstrate the comparison results of simulating natural convection in an open end cavity using different hydrodynamic and thermal boundary conditions. The Prandtl number in the present simulation is 0.71, Rayleigh numbers are 104,105 and 106 and viscosities are selected 0.02 and 0.05. On-Grid bounce-back method with first-order accuracy and non-slip met...

A new method will be introduced for the derivation of thermodynamically consistent boundary conditions for the full Cahn-Hilliard-Navier-Stokes-Fourier system for two immiscible fluids, where the phase field variable (order parameter) is given in terms of concentrations or partial densities. Five different types of models will be presented and discussed. The article can be considered as a conti...

The present paper deals with the effects of Ohmic dissipative Casson fluid flow over a stretching sheet in the presence of aligned magnetic field. The present phenomenon also includes the interaction of thermal radiation and velocity slip. The governing boundary layer equations are transformed into a set of ordinary differential equations using the similarity transformations. The dimensionless ...

A family of eigenfields of a specific Stokes eigenproblem is described which constitute an orthonormal basis of a Sobolev-Hilbert space of incompressible flow fields obeying no-slip boundary conditions. This basis is used to describe a representation theorem for such fields, including spectral formulae for the kinetic energy and the enstrophy. Some other properties of the vorticity and the heli...

in this paper the problem on “magnetic fluid lubrication of porous-pivoted slider bearing with slip velocity by n ahmad et.al.[7]” has been recapitulated using jenkin’s model [4] with the additional effect of squeeze velocity of the above plate. it is found that while discussing the above problem, [7] has stated but ignored the term , where +, in their study (refer equation(2.2)). this paper re...

– Various experiments have found a boundary slip in hydrophobic microchannel flows, but a consistent understanding of the results is still lacking. While Molecular Dynamics (MD) simulations cannot reach the low shear rates and large system sizes of the experiments, it is often impossible to resolve the needed details with macroscopic approaches. We model the interaction between hydrophobic chan...

A new upper bound on the rate of vertical heat transport is established in 3 dimensions for stress-free velocity boundary conditions on horizontally periodic plates. For large (but finite) Prandtl numbers this bound is an improvement over the ‘ultimate’ Ra scaling and in the limit of infinite Pr, agrees with the bound of Ra recently derived in that limit. keywords: Rayleigh-Bénard convection, B...

The generally used model for rotational diffusion, the Perrin-Stokes-Einstein model [l-3] , is based on hydrodynamics with the “stick” boundary condition. That is, the velocity of the solute molecule surface relative to the nearest solvent molecules is zero. Recently Hu and Zwanzig [4] have derived rotational friction coefficients for spheroids with the “slip” boundary condition. Here, the resi...