Stokes' Second Problem with Velocity Slip Boundary Condition

2011 ◽  
Vol 483 ◽  
pp. 287-292 ◽  
Author(s):  
Wei Dong Wang ◽  
Xiang Yu Niu ◽  
Kang Qi Fan ◽  
Qing Yi Wang
Keyword(s):  
Boundary Condition ◽  
Penetration Depth ◽  
Integral Transform ◽  
Separation Of Variables ◽  
Oscillation Amplitude ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Damping Force ◽  
Slip Boundary ◽  
Stokes Second Problem

The damping effect of microfluidics has great effect on the dynamic characteristics of MEMS devices. Based on the separation of variables and the integral transform methods, the Stokes' second problem is solved at the microscale velocity slip boundary condition and the analytical solution for velocity distribution is obtained. Furthermore, the expression of the penetration depth is gotten for Stokes model in this article. Through analysis, it’s found that due to the effect of the microscale velocity slip boundary condition, the velocity oscillation amplitude and the penetration depth have been reduced. Then the shear stress, the damping force and elastic force on the plate have been investigated. It’s shown that both the elastic coefficient and the damping coefficient increases as the oscillation frequency rises.

scholarly journals Slip boundary condition of heat flux in Knudsen layers

2014 ◽  
Vol 470 (2161) ◽  
pp. 20130578 ◽  
Author(s):  
Mingtian Xu
Keyword(s):  
Boundary Condition ◽  
Heat Flux ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Mean Free Path ◽  
Knudsen Layer ◽  
Boltzmann Transport ◽  
Slip Boundary ◽  
The Mean ◽  
Solid Walls

In a Knudsen layer with thickness comparable to the mean free path, collisions between heat carriers and solid walls play an important role in nanoscale heat transports. An interesting question is that whether these collisions also induce the slip of heat flow similar to the velocity slip condition of the rarefied gases on solid walls. In this work based on the discrete Boltzmann transport equation, the slip boundary condition of heat flux on solid walls in the Knudsen layer is established. This result is exemplified by the slip boundary condition of heat flux in nanowires, which has been proposed in a phenomenological way.

Slow Steady Viscous Flow of Newtonian Fluids in Parallel-Disk Viscometer With Wall Slip

2008 ◽  
Vol 75 (4) ◽  
Author(s):  
Y. Leong Yeow ◽  
Yee-Kwong Leong ◽  
Ash Khan
Keyword(s):  
Boundary Condition ◽  
Rheological Properties ◽  
Radial Direction ◽  
Separation Of Variables ◽  
Wall Slip ◽  
Azimuthal Velocity ◽  
Slip Boundary Condition ◽  
Newtonian Fluids ◽  
Parallel Disk ◽  
Slip Boundary

The parallel-disk viscometer is a widely used instrument for measuring the rheological properties of Newtonian and non-Newtonian fluids. The torque-rotational speed data from the viscometer are converted into viscosity and other rheological properties of the fluid under test. The classical no-slip boundary condition is usually assumed at the disk-fluid interface. This leads to a simple azimuthal flow in the disk gap with the azimuthal velocity linearly varying in the radial and normal directions of the disk surfaces. For some complex fluids, the no-slip boundary condition may not be valid. The present investigation considers the flow field when the fluid under test exhibits wall slip. The equation for slow steady azimuthal flow of Newtonian fluids in parallel-disk viscometer in the presence of wall slip is solved by the method of separation of variables. Both linear and nonlinear slip functions are considered. The solution takes the form of a Bessel series. It shows that, in general, as a result of wall slip the azimuthal velocity no longer linearly varies in the radial direction. However, under conditions pertinent to parallel-disk viscometry, it approximately remains linear in the normal direction. The implications of these observations on the processing of parallel-disk viscometry data are discussed. They indicate that the method of Yoshimura and Prud’homme (1988, “Wall Slip Corrections for Couette and Parallel-Disk Viscometers,” J. Rheol., 32(1), pp. 53–67) for the determination of the wall slip function remains valid but the simple and popular procedure for converting the measured torque into rim shear stress is likely to incur significant error as a result of the nonlinearity in the radial direction.

The effect of second order slip condition on MHD nanofluid flow around a semi-circular cylinder

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiahui Cao ◽  
Jing Zhu ◽  
Xinhui Si ◽  
Botong Li
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Condition ◽  
Circular Cylinder ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Second Order ◽  
Ansys Fluent ◽  
Slip Boundary

Abstract Steady forced convection of non-Newtonian nanofluids around a confined semi-circular cylinder subjected to a uniform magnetic field is carried out using ANSYS FLUENT. The numerical solution is obtained using the finite volume method. The user-defined scalar (UDS) is used for the first time to calculate the second order velocity slip boundary condition in semi-circular curved surface and the calculated results are compared with those of the first order velocity slip boundary condition. Besides, the effects of volume fraction, size, type of nanoparticles and magnetic field strength on heat transfer are studied. The present study displays that adding nanoparticles in non-Newtonian fluids significantly enhances heat transfer. In addition, it is observed that the heat transfer rate decreases first and then increases with the increase of Hartmann number. The effects of blocking rate on Nusselt number, wake length and heat transfer effect are shown in the form of graphs or tables.

Experimental Study on Measurement of Tangential Momentum Accommodation Coefficient in Microtube

2010 ◽  
Author(s):  
Hiroki Yamaguchi ◽  
Tsuneo Hanawa ◽  
Oto Yamamoto ◽  
Yu Matsuda ◽  
Yasuhiro Egami ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Knudsen Number ◽  
Mass Flow ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Accommodation Coefficient ◽  
Surface Interaction ◽  
Slip Boundary ◽  
Tangential Momentum Accommodation Coefficient ◽  
Tangential Momentum

Along with the progress in micro- and nano-technologies, such as Micro Electro Mechanical Systems (MEMS) and μ-TAS (Micro-Total Analysis Systems), the Knudsen number, which is a non dimensional parameter for rarefaction, of the flow around and inside the systems becomes large. In such high Knudsen number flows, gas-surface interaction has become important for flow field analyses. To illustrate overall gas-surface interaction without any detailed processes, an accommodation coefficient, α, is the most widely used as an empirical parameter for a practical purpose. One of accommodation coefficients, the tangential momentum accommodation coefficient (TMAC) αt, is in closely related to the loss of the pressure through a micro channel. Therefore, TMAC is an important coefficient for flow inside micro/nano fluidic devices. To obtain TMAC from experiments, the mass flow rate measurements in a microtube were carried out using the constant volume method. The results obtained from the experiments were analyzed in frame of the Navier-Stokes equation associated with the second order velocity slip boundary condition. The mean Knudsen number was less than 0.3, where the velocity slip boundary condition is applicable. From the mass flow rates, the slip coefficient of the boundary condition was obtained, and then, TMAC was determined. The experimental apparatus showed very low leakage rate, and TMAC was determined with a high degree of accuracy. The TMACs of the same surface material with different dimensional parameters were compared for validation of the system.

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