Viscous Slip Coefficient

The coefficients H and S are calculated numerically (see [12]). They depend only on the aspect ratio and can be used with any viscous slip coefficient ap including that obtained for the nondiffuse gas-surface interaction (11) and for gaseous mixtures [18]. The numerical values of H and S are given in Table 1. If the channel is wide, i.e., b > a, then the expression (16) is reduced to... 

Sharipov F, Kalempa D (2003) Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient. Phys Fluid 15(6) 1800-1806... 

Viscous slip coefficient determines the tangential velocity of a gas near a solid surface due to a normal gradient of this velocity. 

The effect of slip flow can be treated either as an extension of a pure viscous flow or as an extension of a Knudsen flow. The simplest method is by adding an additional term (R/2p) (P/RT) dP/dz to Eq. (9.2), with P being the slip coefficient which is proportional to P. 

Figure 1. Variation of transport coefficient with density. Inset depicts the comparison of a purely no-slip viscous theoiy with the NEMD results at l.SO K.

Measurements have been made on a wide variety of molecules adsorbed on Au, Ag, or Pb surfaces [3,4,131,132]. The phase of the adsorbed layer changes from fluid to crystal as the density is increased. As expected, motion of fluid layers produces viscous dissipation that is, the friction vanishes linearly with the sliding velocity. The only surprise is that the ratio between friction and velocity, called the drag coefficient, is orders of magnitude smaller than would be implied by the conventional no-slip boundary condition. When the layer enters an incommensurate phase, the friction retains the viscous form. Not only does the incommensurate crystal shde without measurable static friction, the drag coefficient is as much as an order of magnitude smaller than for the liquid phase ... 

In this lecture, the effects of the abovementioned dimensionless parameters, namely, Knudsen, Peclet, and Brinkman numbers representing rarefaction, axial conduction, and viscous dissipation, respectively, will be analyzed on forced convection heat transfer in microchannel gaseous slip flow under constant wall temperature and constant wall heat flux boundary conditions. Nusselt number will be used as the dimensionless convection heat transfer coefficient. A majority of the results will be presented as the variation of Nusselt number along the channel for various Kn, Pe, and Br values. The lecture is divided into three major sections for convective heat transfer in microscale slip flow. First, the principal results for microtubes will be presented. Then, the effect of roughness on the microchannel wall on heat transfer will be explained. Finally, the variation of the thermophysical properties of the fluid will be considered. 

When the porosity properties of the medium ate reasonably uniform, the permeability coefficient calculated using observed fluxes by rearrangement of Eq. (20.5-2) has a well-defined meaning. For media with fine pores, slip flow in which gas molecules experience wall interactions frequemly as well as gas-gas viscous interactions must be considered. In such cases, the observed permeability coefficient calculated from Eq. (20.5-2) depends on the average pressure Ip = (p, -I- P2)/2] and may be represented by Eq. (20.5-3) ... 

Using the integral transform method, Yu and Ameel [4] solved for Nu for flow in a rectangular microchannel subject to the constant temperature and slip flow boundary conditions. They did not include viscous dissipation in the work, but they included variable thermal accommodation coefficients. Similar to [7], they concluded that Kn, Pr,... 

Here, the coefficient a may be near the Einstein constant for colloidal solution (i.e., 2.5) although the former concerns the energy loss caused by filler in elastic deformation, whereas the latter concerns that in viscous deformation. In large deformation, slip occurs at the interface between filler and adsorbed chains and there may be an overshoot. 

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